Relevant bibliographies by topics / Julia set in a matrix algebra / Journal articles
To see the other types of publications on this topic, follow the link: Julia set in a matrix algebra.

Journal articles on the topic 'Julia set in a matrix algebra'

Author: Grafiati
Published: 7 September 2021
Last updated: 18 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Julia set in a matrix algebra.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Rojas-Rodriguez, Jose C., Ana Y. Aguilar-Bustos, and Eusebio Bugarin. "An O(N) Algorithm for the Computation of the Centroidal Dynamics with Application in the Postural Balance of a Humanoid Robot Using Whole Body Control." International Journal of Humanoid Robotics 18, no. 03 (2021): 2150010. http://dx.doi.org/10.1142/s0219843621500109.

Full text
Abstract:
In this paper, we introduce an [Formula: see text] algorithm for the computation of the centroidal momentum matrix (CMM) and its time derivative using spatial algebra and expressed with Lie algebra operators. The proposed algorithm is applied to the postural balance of a humanoid robot using whole body control with quadratic programming. The employed tasks only require the CMM and its time derivative without the need of the joint space inertia matrix and the Coriolis terms reducing this way the computational cost of the controller. Finally, four simulation scenarios programmed in Julia are considered where several perturbations for the balance of the robot have been taken into account and according to the tracking graphs of the center of mass, centroidal momentum and the trajectories of the center of pressure it is concluded that the performance of the proposed algorithm is satisfactory.
APA, Harvard, Vancouver, ISO, and other styles
2

Zhang, Weijian, and Nicholas J. Higham. "Matrix Depot: an extensible test matrix collection for Julia." PeerJ Computer Science 2 (April 6, 2016): e58. http://dx.doi.org/10.7717/peerj-cs.58.

Full text
Abstract:
Matrix Depot is a Julia software package that provides easy access to a large and diverse collection of test matrices. Its novelty is threefold. First, it is extensible by the user, and so can be adapted to include the user’s own test problems. In doing so, it facilitates experimentation and makes it easier to carry out reproducible research. Second, it amalgamates in a single framework two different types of existing matrix collections, comprising parametrized test matrices (including Hansen’s set of regularization test problems and Higham’s Test Matrix Toolbox) and real-life sparse matrix data (giving access to the University of Florida sparse matrix collection). Third, it fully exploits the Julia language. It uses multiple dispatch to help provide a simple interface and, in particular, to allow matrices to be generated in any of the numeric data types supported by the language.
APA, Harvard, Vancouver, ISO, and other styles
3

Devaney, Robert L., and Daniel M. Look. "Symbolic dynamics for a Sierpinski curve Julia set." Journal of Difference Equations and Applications 11, no. 7 (2005): 581–96. http://dx.doi.org/10.1080/10236190412331334473.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Rivera-Letelier, Juan. "On the continuity of Hausdorff dimension of Julia sets and similarity between the Mandelbrot set and Julia sets." Fundamenta Mathematicae 170, no. 3 (2001): 287–317. http://dx.doi.org/10.4064/fm170-3-6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Domínguez, P., A. Hernández, and G. Sienra. "Residual Julia set for functions with the Ahlfors' Property." Journal of Difference Equations and Applications 20, no. 7 (2014): 1019–32. http://dx.doi.org/10.1080/10236198.2014.884084.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Rudhito, Marcellinus Andy, Sri Wahyuni, Ari Suparwanto, and Frans Susilo. "Matriks atas Aljabar Max-Plus Interval." Jurnal Natur Indonesia 13, no. 2 (2012): 94. http://dx.doi.org/10.31258/jnat.13.2.94-99.

Full text
Abstract:
This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) and a method tosimplify the computation of the operation of them. This matrix algebra is an extension of matrix algebra over max-plus algebra and can be used to discuss the matrix algebra over fuzzy number max-plus algebra via its alpha-cut.The finding shows that the set of all interval matrices together with the max-plus scalar multiplication operationand max-plus addition is a semimodule. The set of all square matrices over max-plus algebra together with aninterval of max-plus addition operation and max-plus multiplication operation is a semiring idempotent. As reasoningfor the interval matrix operations can be performed through the corresponding matrix interval, because thatsemimodule set of all interval matrices is isomorphic with semimodule the set of corresponding interval matrix,and the semiring set of all square interval matrices is isomorphic with semiring the set of the correspondingsquare interval matrix.
APA, Harvard, Vancouver, ISO, and other styles
7

Aspenberg, Magnus. "Rational Misiurewicz maps for which the Julia set is not the whole sphere." Fundamenta Mathematicae 206 (2009): 41–48. http://dx.doi.org/10.4064/fm206-0-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Hawkins, Jane. "A family of elliptic functions with Julia set the whole sphere." Journal of Difference Equations and Applications 16, no. 5-6 (2010): 597–612. http://dx.doi.org/10.1080/10236190903257859.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Hireš, Máté, Monika Molnárová, and Peter Drotár. "Robustness of Interval Monge Matrices in Fuzzy Algebra." Mathematics 8, no. 4 (2020): 652. http://dx.doi.org/10.3390/math8040652.

Full text
Abstract:
Max–min algebra (called also fuzzy algebra) is an extremal algebra with operations maximum and minimum. In this paper, we study the robustness of Monge matrices with inexact data over max–min algebra. A matrix with inexact data (also called interval matrix) is a set of matrices given by a lower bound matrix and an upper bound matrix. An interval Monge matrix is the set of all Monge matrices from an interval matrix with Monge lower and upper bound matrices. There are two possibilities to define the robustness of an interval matrix. First, the possible robustness, if there is at least one robust matrix. Second, universal robustness, if all matrices are robust in the considered set of matrices. We found necessary and sufficient conditions for universal robustness in cases when the lower bound matrix is trivial. Moreover, we proved necessary conditions for possible robustness and equivalent conditions for universal robustness in cases where the lower bound matrix is non-trivial.
APA, Harvard, Vancouver, ISO, and other styles
10

FISHBACK, PAUL E., and MATTHEW D. HORTON. "QUADRATIC DYNAMICS IN MATRIX RINGS: TALES OF TERNARY NUMBER SYSTEMS." Fractals 13, no. 02 (2005): 147–56. http://dx.doi.org/10.1142/s0218348x05002787.

Full text
Abstract:
We describe the quadratic dynamics in certain three-component number systems, which like the complex numbers, can be expressed as rings of real matrices. This description is accomplished using the properties of the real quadratic family and its various first- and second-order phase and parameter derivatives. We demonstrate that the fundamental dichotomy of defining the Mandelbrot set either in terms of filled Julia sets or in terms of the orbit of the origin extends to these ternary number systems.
APA, Harvard, Vancouver, ISO, and other styles
11

Nekrashevych, Volodymyr. "The Julia set of a post-critically finite endomorphism of $\mathbb{PC}^2$." Journal of Modern Dynamics 6, no. 3 (2012): 327–75. http://dx.doi.org/10.3934/jmd.2012.6.327.

Full text
APA, Harvard, Vancouver, ISO, and other styles
12

Michailidou, Christina, and Panayiotis Psarrakos. "Gershgorin type sets for eigenvalues of matrix polynomials." Electronic Journal of Linear Algebra 34 (February 21, 2018): 652–74. http://dx.doi.org/10.13001/1081-3810.3763.

Full text
Abstract:
New localization results for polynomial eigenvalue problems are obtained, by extending the notions of the Gershgorin set, the generalized Gershgorin set, the Brauer set and the Dashnic-Zusmanovich set to the case of matrix polynomials.
APA, Harvard, Vancouver, ISO, and other styles
13

Sivakumar, B. "MATRIX UNITS FOR THE GROUP ALGEBRA kGf = k((ℤ2 × ℤ2) ≀ Sf)". Asian-European Journal of Mathematics 02, № 02 (2009): 255–77. http://dx.doi.org/10.1142/s1793557109000212.

Full text
Abstract:
The irreducible representations of the group Gf := (ℤ2 × ℤ2) ≀ Sf are indexed by 4-partitions of f, i.e., by the set {[α]3[β]2[γ]1[δ]0|α ⊢ u3, β ⊢ u2, γ ⊢ u1, δ ⊢ u0, u0 + u1 + u2 + u3 = f}. This set is in 1 - 1 correspondence with partitions of 4f whose 4-core is empty. In this paper we construct the inequivalent irreducible representations of Gf. We also compute a complete set of seminormal matrix units for the group algebra kGf.
APA, Harvard, Vancouver, ISO, and other styles
14

Stankewitz, Rich. "Density of repelling fixed points in the Julia set of a rational or entire semigroup." Journal of Difference Equations and Applications 16, no. 5-6 (2010): 763–71. http://dx.doi.org/10.1080/10236190903203929.

Full text
APA, Harvard, Vancouver, ISO, and other styles
15

Liu, Dong Li. "The Equivalence Relationship of Matrix and the Corresponding Equivalence Classes." Applied Mechanics and Materials 651-653 (September 2014): 2211–15. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.2211.

Full text
Abstract:
In order to further integrate the content of Linear Algebra, and deeply reveal the equivalence relationship of matrix, this paper discusses the three equivalence relationships on the set of matrices: matrix equivalence、matrix similarity and matrix contract, and gives the corresponding equivalence classes, which further enriches the theory of Linear Algebra.
APA, Harvard, Vancouver, ISO, and other styles
16

HUANG, WEN-JUI. "NONLOCAL MATRIX GENERALIZATIONS OF N=2 SUPER VIRASORO ALGEBRA." Modern Physics Letters A 09, no. 36 (1994): 3347–58. http://dx.doi.org/10.1142/s0217732394003178.

Full text
Abstract:
We study the generalization of the second Gelfand-Dickey bracket to the superdifferential operators with matrix-valued coefficients. The associated matrix Miura transformation is derived. Using this bracket we work out a nonlocal and nonlinear N=2 superalgebra which contains the N=2 super Virasoro algebra as a subalgebra. The bosonic limit of this superalgebra is considered. We show that when the spin-1 fields in this bosonic algebra are set to zero the resulting Dirac bracket gives precisely the recently derived V2,2 algebra.
APA, Harvard, Vancouver, ISO, and other styles
17

Fares, Ali, Ali Ayad, and Bruno de Malafosse. "Calculations on Matrix Transformations Involving an Infinite Tridiagonal Matrix." Axioms 10, no. 3 (2021): 218. http://dx.doi.org/10.3390/axioms10030218.

Full text
Abstract:
Given any sequence z=znn≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y=ynn≥1 such that y/z=yn/znn≥1∈E; in particular, sz0 denotes the set of all sequences y such that y/z tends to zero. Here, we consider the infinite tridiagonal matrix Br,s,t˜, obtained from the triangle Br,s,t, by deleting its first row. Then we determine the sets of all positive sequences a=ann≥1 such that EaBr,s,t˜⊂Ea, where E=ℓ∞, c0, or c. These results extend some recent results.
APA, Harvard, Vancouver, ISO, and other styles
18

Barthels, Henrik, Christos Psarras, and Paolo Bientinesi. "Linnea." ACM Transactions on Mathematical Software 47, no. 3 (2021): 1–26. http://dx.doi.org/10.1145/3446632.

Full text
Abstract:
The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for matrix computations (e.g., Matlab, Eigen) internally use optimized kernels such as those provided by BLAS and LAPACK; however, their translation algorithms are often too simplistic and thus lead to a suboptimal use of said kernels, resulting in significant performance losses. To combine the productivity offered by high-level languages, and the performance of low-level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem; as output, it returns an efficient sequence of calls to high-performance kernels. Linnea uses a custom best-first search algorithm to find a first solution in less than a second, and increasingly better solutions when given more time. In 125 test problems, the code generated by Linnea almost always outperforms Matlab, Julia, Eigen, and Armadillo, with speedups up to and exceeding 10×.
APA, Harvard, Vancouver, ISO, and other styles
19

Karpińska, Bogusława. "Area and Hausdorff dimension of the set of accessible points of the Julia sets of $λe^z$ and $λ \sin(z)$". Fundamenta Mathematicae 159, № 3 (1999): 269–87. http://dx.doi.org/10.4064/fm_1999_159_3_1_269_287.

Full text
APA, Harvard, Vancouver, ISO, and other styles
20

Siswanto, Ari Suparwanto, and M. Andy Rudhito. "OPTIMIZING RANGE NORM OF THE IMAGE SET OF MATRIX OVER INTERVAL MAX-PLUS ALGEBRA." Far East Journal of Mathematical Sciences (FJMS) 99, no. 1 (2015): 17–32. http://dx.doi.org/10.17654/ms099010017.

Full text
APA, Harvard, Vancouver, ISO, and other styles
21

Sedighi Hafshejani, J., A. R. Naghipour, and M. R. Rismanchian. "Integer-valued polynomials over block matrix algebras." Journal of Algebra and Its Applications 19, no. 03 (2019): 2050053. http://dx.doi.org/10.1142/s021949882050053x.

Full text
Abstract:
In this paper, we state a generalization of the ring of integer-valued polynomials over upper triangular matrix rings. The set of integer-valued polynomials over some block matrix rings is studied. In fact, we consider the set of integer-valued polynomials [Formula: see text] for each [Formula: see text], where [Formula: see text] is an integral domain with quotient field [Formula: see text] and [Formula: see text] is a block matrix ring between upper triangular matrix ring [Formula: see text] and full matrix ring [Formula: see text]. In fact, we have [Formula: see text]. It is known that the sets of integer-valued polynomials [Formula: see text] and [Formula: see text] are rings. We state some relations between the rings [Formula: see text] and the partitions of [Formula: see text]. Then, we show that the set [Formula: see text] is a ring for each [Formula: see text]. Further, it is proved that if the ring [Formula: see text] is not Noetherian then the ring [Formula: see text] is not Noetherian, too. Finally, some properties and relations are stated between the rings [Formula: see text], [Formula: see text] and [Formula: see text].
APA, Harvard, Vancouver, ISO, and other styles
22

Song, Haizhou, and Wang Qiufen. "Property and Representation of n-Order Pythagorean Matrix." Mathematical Problems in Engineering 2020 (March 24, 2020): 1–10. http://dx.doi.org/10.1155/2020/2857417.

Full text
Abstract:
Here we study the character and expression of n-order Pythagorean matrix using number theory. Theories of Pythagorean matrix are obtained. Using related algebra skills, we prove that the set which constitutes all n-order Pythagorean matrices is a finitely generated group of matrix multiplication and gives a generated tuple of this finitely generated group (n≤10) simultaneously.
APA, Harvard, Vancouver, ISO, and other styles
23

Kokabifar, E., G. B. Loghmani, and Panayiotis Psarrakos. "On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue." Electronic Journal of Linear Algebra 31 (February 5, 2016): 71–86. http://dx.doi.org/10.13001/1081-3810.2921.

Full text
Abstract:
Consider an$n\times n matrix polynomial P(\lambda). An upper bound for a spectral norm distance from P(\lambda) to the set of n \times n matrix polynomials that have a given scalar μ in C as a multiple eigenvalue was obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modified method is developed and its efficiency is verified by two illustrative examples. The proposed methodology can also be applied to general matrix polynomials.
APA, Harvard, Vancouver, ISO, and other styles
24

KYE, SEUNG-HYEOK. "On the convex set of completely positive linear maps in matrix algebras." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 1 (1997): 45–54. http://dx.doi.org/10.1017/s0305004196001508.

Full text
Abstract:
Let PI (respectively CPI) be the convex compact set of all unital positive (respectively completely positive) linear maps from the matrix algebra Mm([Copf ]) into Mn([Copf ]). We show that maximal faces of CPI correspond to one dimensional subspaces of the vector space Mm, n([Copf ]). Furthermore, a maximal face of CPI lies on the boundary of PI if and only if the corresponding subspace is generated by a rank one matrix.
APA, Harvard, Vancouver, ISO, and other styles
25

Serfati, Michel. "A Note on Postian Matrix Theory." International Journal of Algebra and Computation 07, no. 02 (1997): 161–79. http://dx.doi.org/10.1142/s0218196797000101.

Full text
Abstract:
The present paper is devoted to some aspects of postian matrix theory over an arbitrary Post algebra, through results in Postian relative–pseudocomplementation. It is well known (for instance Rousseau [10] or Dwinger [6]) that any r-Post algebra is a Brouwerian lattice (or a Heyting algebra), that is to say, for every (a, b) in P2, the set of x in P such as a. x ≤ b admits a greatest element (a.x is inf {a, x}), called the relative inf–pseudocomplement of a in b, and denoted (b|a). In the first part of our paper, we compute the explicit expression of the disjunctive components of the relative inf–pseudocomplement (Theorem 2), which allows us to state some specific new properties of Postian pseudocomplementation, among which the cases where (b|a) is a Boolean element, and the equation (x|a) = c (Theorem 4), for which we give a consistency condition. Relative pseudo complementation in fact plays a major role in Postian structures, since we show (Theorem 5), that every element a in P is completely determined by the sequence of the (ek|a): in fact, being given (r-1) elements of P submitted to the ascending chain condition: α1 ≤ α2 ≤ … ≤ αr-1, there exists exactly one a in P such as (ek|a) = αk for every k, where the ek are the elements of the underlying chain in P. Study of pseudocomplementation properties in some Post algebra P actually helps us to enlighten relations between P and, on one hand, its center B (the set of its complemented elements, which is a Boolean algebra), on the other hand, the underlying chain. The second part is devoted to Postian linear matrix equations and inequations: in fact just like in Boolean algebras, the existence of the inf–pseudocomplement in the underlying lattice implies the residuation property is valid over the ordered semi-group of Postian matrices, equipped with the matrix product ⊗ (this was a general theorem from Blyth [3]): the Postian matrix inequation A ⊗ X ≤ B thus admits a greatest solution (Theorem 6), which is explicitly computed. This provides a consistency condition for the matrix equation A ⊗ X = B (Theorem 7). Another result states a characterization of inversible square Postian matrices. On this point of inversibility, as it is well known, the Boolean results were built in three successive steps by Wedderbrun [17], Luce [9] and Rutherford [13]. As to the Postian case, we prove in turn that a Postian matrix is inversible if and only if it is Boolean and orthogonal (Theorem 11). To prove this result, as well as Theorem 2 in the first part, we make a systematic use of the representation theorem for Post algebras by the Boolean way, as enunciated in the Preliminaries (Theorem 1). Repeated applications of the method provide a large set of conditions equivalent to the inversibility of a Postian matrix (Theorem 12). Afterwards, we examine various other Postian matrix equations and inequations, among which t A ⊗ A ≤ I, leading to the characterization of right–distributive over conjunction–Postian matrices (Theorem 9), and also the equation A ⊗ X = Ek, for which it is given a complete consistency condition (Theorem 13).
APA, Harvard, Vancouver, ISO, and other styles
26

Li, Chi-Kwong, and Ahmed Ramzi Sourour. "Linear Operators on Matrix Algebras that Preserve the Numerical Range, Numerical Radius or the States." Canadian Journal of Mathematics 56, no. 1 (2004): 134–67. http://dx.doi.org/10.4153/cjm-2004-007-4.

Full text
Abstract:
AbstractEvery norm v on Cn induces two norm numerical ranges on the algebra Mn of all n × n complex matrices, the spatial numerical rangewhere vD is the norm dual to v, and the algebra numerical rangewhere is the set of states on the normed algebra Mn under the operator norm induced by v. For a symmetric norm v, we identify all linear maps on Mn that preserve either one of the two norm numerical ranges or the set of states or vector states. We also identify the numerical radius isometries, i.e., linear maps that preserve the (one) numerical radius induced by either numerical range. In particular, it is shown that if v is not the ℓ1, ℓ2, or ℓ∞ norms, then the linear maps that preserve either numerical range or either set of states are “inner”, i.e., of the formA ⟼ Q*AQ, where Q is a product of a diagonal unitary matrix and a permutation matrix and the numerical radius isometries are unimodular scalar multiples of such inner maps. For the ℓ1 and the ℓ∞ norms, the results are quite different.
APA, Harvard, Vancouver, ISO, and other styles
27

Kinani, E. H. El, and M. Zakkari. "q-Area Preserving Algebras SDiff(Tk) and the Matrix Algebra $\bar a_{\infty}$." Modern Physics Letters A 12, no. 12 (1997): 821–25. http://dx.doi.org/10.1142/s0217732397000844.

Full text
Abstract:
We consider the infinite matrix Lie algebra [Formula: see text] and an infinite set of its subalgebras parametrized by an Nth root of the unity; qN=1. We obtain the embedding in [Formula: see text] of the area preserving diffeomorphism on the 2-D torus and also its one-parameter deformed version. The correspondence between the area preserving diffeomorphism on the torus Tk, k>2 and the algebra [Formula: see text] is pointed out.
APA, Harvard, Vancouver, ISO, and other styles
28

Johnson, Charles, J. Pena, and Tomasz Szulc. "Optimal Gersgorin-style estimation of the largest singular value. II." Electronic Journal of Linear Algebra 31 (February 5, 2016): 679–85. http://dx.doi.org/10.13001/1081-3810.3033.

Full text
Abstract:
In estimating the largest singular value in the class of matrices equiradial with a given $n$-by-$n$ complex matrix $A$, it was proved that it is attained at one of $n(n-1)$ sparse nonnegative matrices (see C.R.~Johnson, J.M.~Pe{\~n}a and T.~Szulc, Optimal Gersgorin-style estimation of the largest singular value; {\em Electronic Journal of Linear Algebra Algebra Appl.}, 25:48--59, 2011). Next, some circumstances were identified under which the set of possible optimizers of the largest singular value can be further narrowed (see C.R.~Johnson, T.~Szulc and D.~Wojtera-Tyrakowska, Optimal Gersgorin-style estimation of the largest singular value, {\it Electronic Journal of Linear Algebra Algebra Appl.}, 25:48--59, 2011). Here the cardinality of the mentioned set for $n$-by-$n$ matrices is further reduced. It is shown that the largest singular value, in the class of matrices equiradial with a given $n$-by-$n$ complex matrix, is attained at one of $n(n-1)/2$ sparse nonnegative matrices. Finally, an inequality between the spectral radius of a $3$-by-$3$ nonnegative matrix $X$ and the spectral radius of a modification of $X$ is also proposed.
APA, Harvard, Vancouver, ISO, and other styles
29

Crabb, M. J., and W. D. Munn. "On the l1-algebra of certain monoids." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 5 (1998): 1023–31. http://dx.doi.org/10.1017/s0308210500030043.

Full text
Abstract:
The monoids considered are the free monoid Mx and the free monoid-with-involution MIx on a nonempty set X. In each case, relative to a simply-defined involution, an explicit construction is given for a separating family of continuous star matrix representations of the l1-algebra of the monoid and it is shown that this algebra admits a faithful trace. The results are based on earlier work by M. J. Crabb et al. concerning the complex semigroup algebras of Mx and MIx.
APA, Harvard, Vancouver, ISO, and other styles
30

Councilman, Samuel. "Sharing Teaching Ideas: Bisymmetric Matrices: Some Elementary New Problems." Mathematics Teacher 82, no. 8 (1989): 622–23. http://dx.doi.org/10.5951/mt.82.8.0622.

Full text
Abstract:
In introductory linear algebra courses one continually seeks interesting sets of matrices that are closed under the operations of matrix addition, scalar multiplication, and if possible, matrix multiplication. Most texts mention symmetric and antisymmetric matrices and ask the reader to show that these sets are closed under matrix addition and scalar multiplication but fail to be closed under matrix multiplication. Few textbooks, if any, suggest an investigation of the set of matrices that are symmetric with respect to both diagonals, namely bisymmetric matrices. The following is a sequence of relatively straightforward problems that can be used as homework, class discussion, or even examination material in elementary linear algebra classes.
APA, Harvard, Vancouver, ISO, and other styles
31

Kye, Seung-Hyeok. "Facial Structures for the Positive Linear Maps Between Matrix Algebras." Canadian Mathematical Bulletin 39, no. 1 (1996): 74–82. http://dx.doi.org/10.4153/cmb-1996-010-x.

Full text
Abstract:
AbstractLet denote the convex set of all positive linear maps from the matrix algebra Mn(ℂ) into itself. We construct a join homomorphism from the complete lattice of all faces of into the complete lattice of all join homomorphisms between the lattice of all subspaces of ℂn . We also characterize all maximal faces of .
APA, Harvard, Vancouver, ISO, and other styles
32

Ballico, Edoardo. "The Hermitian Null-range of a Matrix over a Finite Field." Electronic Journal of Linear Algebra 34 (February 21, 2018): 205–16. http://dx.doi.org/10.13001/1081-3810.3416.

Full text
Abstract:
Let $q$ be a prime power. For $u=(u_1,\dots ,u_n), v=(v_1,\dots ,v_n)\in \mathbb {F} _{q^2}^n$, let $\langle u,v\rangle := \sum _{i=1}^{n} u_i^qv_i$ be the Hermitian form of $\mathbb {F} _{q^2}^n$. Fix an $n\times n$ matrix $M$ over $\mathbb {F} _{q^2}$. In this paper, it is considered the case $k=0$ of the set $\mathrm{Num} _k(M):= \{\langle u,Mu\rangle \mid u\in \mathbb {F} _{q^2}^n, \langle u,u\rangle =k\}$. When $M$ has coefficients in $\mathbb {F} _q$ the paper studies the set $\mathrm{Num} _k(M)_q:= \{\langle u,Mu\rangle \mid u\in \mathbb {F} _q^n,\langle u,u\rangle =k\}\subseteq \mathbb {F} _q$. The set $\mathrm{Num} _1(M)$ is the numerical range of $M$, previously introduced in a paper by Coons, Jenkins, Knowles, Luke, and Rault (case $q$ a prime $p\equiv 3\pmod{4}$), and by the author (arbitrary $q$). In this paper, it is studied in details $\mathrm{Num} _0(M)$ and $\mathrm{Num} _k(M)_q$ when $n=2$. If $q$ is even, $\mathrm{Num} _0(M)_q$ is easily described for arbitrary $n$. If $q$ is odd, then either $\mathrm{Num} _0(M)_q =\{0\}$, or $\mathrm{Num} _0(M)_q=\mathbb {F} _q$, or $\sharp (\mathrm{Num} _0(M)_q)=(q+1)/2$.
APA, Harvard, Vancouver, ISO, and other styles
33

MADORE, J. "ALGEBRAIC STRUCTURE AND PARTICLE SPECTRA." International Journal of Modern Physics A 06, no. 08 (1991): 1287–300. http://dx.doi.org/10.1142/s0217751x91000678.

Full text
Abstract:
In previous articles classical gauge theory was studied with a matrix algebra as an additional noncommutative factor in the algebra of classical observables. The extra derivations permitted a unification in a common multiplet of a set of Higgs fields with the gauge potentials. In the present article the algebra of derivations is modified in order to obtain a theory which is closer to a realistic physical model.
APA, Harvard, Vancouver, ISO, and other styles
34

Wang, Xiaoxiao, Chaoqian Li, and Yaotang Li. "A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices." Open Mathematics 16, no. 1 (2018): 298–310. http://dx.doi.org/10.1515/math-2018-0030.

Full text
Abstract:
AbstractA set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues.
APA, Harvard, Vancouver, ISO, and other styles
35

Schwartz, David I., and Stuart S. Chen. "A constraint-based approach for qualitative matrix structural analysis." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 9, no. 1 (1995): 23–36. http://dx.doi.org/10.1017/s0890060400002067.

Full text
Abstract:
AbstractQualitative physics, a subfield of artificial intelligence, adapts intuitive and non-numerical reasoning for descriptive analysis of physical systems. The application of a set-based qualitative algebra to matrix analysis (QMA) allows for the development of a qualitative matrix stiffness methodology for linear elastic structural analysis. The unavoidable introduction of arithmetic ambiguity requires the reinforcement of physical constraints complementary to standard matrix operations. The overall analysis technique incorporates such constraints within the set-based framework with logic programming. Truss, beam, and frame structures demonstrate constraint relationships, which prune spurious solutions resulting from qualitative arithmetic relations. Though QMA is not a panacea for all structural applications, it provides greater insight into new notions of physical analysis.
APA, Harvard, Vancouver, ISO, and other styles
36

Hong, Shaofang, K. P. Shum, and Qi Sun. "On Nonsingular Power LCM Matrices." Algebra Colloquium 13, no. 04 (2006): 689–704. http://dx.doi.org/10.1142/s1005386706000642.

Full text
Abstract:
Let e ≥ 1 be an integer and S={x1,…,xn} a set of n distinct positive integers. The matrix ([xi, xj]e) having the power [xi, xj]e of the least common multiple of xi and xj as its (i, j)-entry is called the power least common multiple (LCM) matrix defined on S. The set S is called gcd-closed if (xi,xj) ∈ S for 1≤ i, j≤ n. Hong in 2004 showed that if the set S is gcd-closed such that every element of S has at most two distinct prime factors, then the power LCM matrix on S is nonsingular. In this paper, we use Hong's method developed in his previous papers to consider the next case. We prove that if every element of an arbitrary gcd-closed set S is of the form pqr, or p2qr, or p3qr, where p, q and r are distinct primes, then except for the case e=1 and 270, 520 ∈ S, the power LCM matrix on S is nonsingular. We also show that if S is a gcd-closed set satisfying xi< 180 for all 1≤ i≤ n, then the power LCM matrix on S is nonsingular. This proves that 180 is the least primitive singular number. For the lcm-closed case, we establish similar results.
APA, Harvard, Vancouver, ISO, and other styles
37

Hews, Joshua, and Leo Livshits. "Groups of Matrices That Act Monopotently." Electronic Journal of Linear Algebra 32 (February 6, 2017): 423–37. http://dx.doi.org/10.13001/1081-3810.3479.

Full text
Abstract:
In the present article, the authors continue the line of inquiry started by Cigler and Jerman, who studied the separation of eigenvalues of a matrix under an action of a matrix group. The authors consider groups \Fam{G} of matrices of the form $\left[\small{\begin{smallmatrix} G & 0\\ 0& z \end{smallmatrix}}\right]$, where $z$ is a complex number, and the matrices $G$ form an irreducible subgroup of $\GL(\C)$. When \Fam{G} is not essentially finite, the authors prove that for each invertible $A$ the set $\Fam{G}A$ contains a matrix with more than one eigenvalue. The authors also consider groups $\Fam{G}$ of matrices of the form $\left[\small{\begin{smallmatrix} G & x\\ 0& 1 \end{smallmatrix}}\right]$, where the matrices $G$ comprise a bounded irreducible subgroup of $\GL(\C)$. When \Fam{G} is not finite, the authors prove that for each invertible $A$ the set $\Fam{G}A$ contains a matrix with more than one eigenvalue.
APA, Harvard, Vancouver, ISO, and other styles
38

ARVESON, WILLIAM, and GEOFFREY PRICE. "THE STRUCTURE OF SPIN SYSTEMS." International Journal of Mathematics 14, no. 02 (2003): 119–37. http://dx.doi.org/10.1142/s0129167x03001673.

Full text
Abstract:
A spin system is a sequence of self-adjoint unitary operators U1, U2, … acting on a Hilbert space H which either commute or anticommute, UiUj = ±UjUi for all i, j; it is called irreducible when {U1, U2, …} is an irreducible set of operators. There is a unique infinite matrix (cij) with 0, 1 entries satisfying [Formula: see text] Every matrix (cij) with 0, 1 entries satisfying cij = cji and cii = 0 arises from a nontrivial irreducible spin system, and there are uncountably many such matrices. In cases where the commutation matrix (cij) is of "infinite rank" (these are the ones for which infinite dimensional irreducible representations exist), we show that the C*-algebra generated by an irreducible spin system is the CAR algebra, an infinite tensor product of copies of [Formula: see text], and we classify the irreducible spin systems associated with a given matrix (cij) up to approximate unitary equivalence. That follows from a structural result. The C*-algebra generated by the universal spin system u1, u2, … of (cij) decomposes into a tensor product [Formula: see text], where X is a Cantor set (possibly finite) and [Formula: see text] is either the CAR algebra or a finite tensor product of copies of [Formula: see text]. We describe the nature of this decomposition in terms of the "symplectic" properties of the ℤ2-valued form [Formula: see text]x, y ranging over the free infninite dimensional vector space over the Galois field ℤ2.
APA, Harvard, Vancouver, ISO, and other styles
39

Franca, Willian, and Nelson Louza. "Generalized Commuting Maps On The Set of Singular Matrices." Electronic Journal of Linear Algebra 35 (December 5, 2019): 533–42. http://dx.doi.org/10.13001/ela.2019.5173.

Full text
Abstract:
Let Mn(K) be the ring of all n × n matrices over a field K. In the present paper, additive mappings G : Mn(K) → Mn(K) such that [[G(y), y], y] = 0 for all singular matrix y will be characterized. Precisely, it will be proved that G(x) = λx + µ(x) for all x ∈ Mn(K), where λ ∈ K and µ is a central map. As an application, the description is given of all additive maps g : Mn(K) → Mn(K) such that [[g(yk1 ), yk2 ], yk3 ] = 0 for all singular matrices y ∈ Mn(K), where m ∈ N∗.
APA, Harvard, Vancouver, ISO, and other styles
40

BROWN, JONATHAN, and JONATHAN BRUNDAN. "ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES." Journal of the Australian Mathematical Society 86, no. 1 (2009): 1–15. http://dx.doi.org/10.1017/s1446788708000608.

Full text
Abstract:
AbstractWe construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.
APA, Harvard, Vancouver, ISO, and other styles
41

Bünger, Florian, and Siegfried Rump. "The determinant of a complex matrix and Gershgorin circles." Electronic Journal of Linear Algebra 35 (February 1, 2019): 181–86. http://dx.doi.org/10.13001/1081-3810.3910.

Full text
Abstract:
Each connected component of the Gershgorin circles of a matrix contains exactly as many eigenvalues as circles are involved. Thus, the Minkowski (set) product of all circles contains the determinant if all circles are disjoint. In [S.M. Rump. Bounds for the determinant by Gershgorin circles. Linear Algebra and its Applications, 563:215--219, 2019.], it was proved that statement to be true for real matrices whose circles need not to be disjoint. Moreover, it was asked whether the statement remains true for complex matrices. This note answers that in the affirmative. As a by-product, a parameterization of the outer loop of a Cartesian oval without case distinction is derived.
APA, Harvard, Vancouver, ISO, and other styles
42

Das, Himadri Lal, and M. Rajesh Kannan. "On the dense subsets of matrices with distinct eigenvalues and distinct singular values." Electronic Journal of Linear Algebra 36, no. 36 (2020): 834–46. http://dx.doi.org/10.13001/ela.2020.5329.

Full text
Abstract:
It is well known that the set of all $n \times n$ matrices with distinct eigenvalues is a dense subset of the set of all real or complex $n \times n$ matrices. In [D.J. Hartfiel. Dense sets of diagonalizable matrices. {\em Proceedings of the American Mathematical Society}, 123(6):1669--1672, 1995.], the author established a necessary and sufficient condition for a subspace of the set of all $n \times n$ matrices to have a dense subset of matrices with distinct eigenvalues. The objective of this article is to identify necessary and sufficient conditions for a subset of the set of all $n \times n$ real or complex matrices to have a dense subset of matrices with distinct eigenvalues. Some results of Hartfiel are extended, and the existence of dense subsets of matrices with distinct singular values in the subsets of the set of all real or complex matrices is studied. Furthermore, for a matrix function $F(x)$, defined on a closed and bounded interval whose entries are analytic functions, it is proved that the set of all points for which the matrix $F(x)$ has repeated analytic eigenvalues/analytic singular values is either a finite set or the whole domain of the function $F$.
APA, Harvard, Vancouver, ISO, and other styles
43

Sasane, Amol. "An analogue of Serre’s conjecture for a ring of distributions." Topological Algebra and its Applications 8, no. 1 (2020): 88–91. http://dx.doi.org/10.1515/taa-2020-0100.

Full text
Abstract:
AbstractThe set 𝒜 := 𝔺δ0+ 𝒟+′, obtained by attaching the identity δ0 to the set 𝒟+′ of all distributions on 𝕉 with support contained in (0, ∞), forms an algebra with the operations of addition, convolution, multiplication by complex scalars. It is shown that 𝒜 is a Hermite ring, that is, every finitely generated stably free 𝒜-module is free, or equivalently, every tall left-invertible matrix with entries from 𝒜 can be completed to a square matrix with entries from 𝒜, which is invertible.
APA, Harvard, Vancouver, ISO, and other styles
44

Kribs, David, Jeremy Levick, and Rajesh Pereira. "Totally Positive Density Matrices and Linear Preservers." Electronic Journal of Linear Algebra 31 (February 5, 2016): 313–20. http://dx.doi.org/10.13001/1081-3810.3129.

Full text
Abstract:
The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Higher dimensional cases are also discussed.
APA, Harvard, Vancouver, ISO, and other styles
45

Mairesse, Jean. "Products of Irreducible Random Matrices in the (Max, +) Algebra." Advances in Applied Probability 29, no. 2 (1997): 444–77. http://dx.doi.org/10.2307/1428012.

Full text
Abstract:
We consider the recursive equation x(n + 1)= A(n)⊗x(n), where x(n + 1) and x(n) are ℝk-valued vectors and A(n) is an irreducible random matrix of size k × k. The matrix-vector multiplication in the (max, +) algebra is defined by (A(n)⊗x(n))= maxj (Aij (n) + xj(n)). This type of equation can be used to represent the evolution of stochastic event graphs which include cyclic Jackson networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the sequence {A(n), n ∈ ℕ} is i.i.d. or, more generally, stationary and ergodic. The main result of the paper states that the system couples in finite time with a unique stationary regime if and only if there exists a set of matrices such that and the matrices have a unique periodic regime.
APA, Harvard, Vancouver, ISO, and other styles
46

Feng, Lianggui, and Wei Cheng. "The Solution Set to the Quaternion Matrix Equation $AX-\overline{X}B=0$." Algebra Colloquium 19, no. 01 (2012): 175–80. http://dx.doi.org/10.1142/s1005386712000132.

Full text
APA, Harvard, Vancouver, ISO, and other styles
47

Jiang, Zhaolin, Tingting Xu, and Fuliang Lu. "Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/418194.

Full text
Abstract:
The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra ofn×ncomplex skew-circulant matrices are displayed in this paper.
APA, Harvard, Vancouver, ISO, and other styles
48

Parthasarathy, K. R. "Extreme Points of the Convex set of Stochastic Maps on A C*-Algebra." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 04 (1998): 599–609. http://dx.doi.org/10.1142/s0219025798000326.

Full text
Abstract:
Let [Formula: see text] be a unital C*-subalgebra of the C*-algebra ℬ(ℋ) of all bounded operators on a complex separable Hilbert space ℋ. Let [Formula: see text] denote the convex set of all unital, linear, completely positive and normal maps of [Formula: see text] into itself. Using Stinespring's theorem, we present a criterion for an element [Formula: see text] to be extremal. When [Formula: see text], this criterion leads to an explicit description of the set of all extreme points of [Formula: see text]. We also obtain a quantum probabilistic analogue of the classical Birkhoff's theorem2 that every bistochastic matrix can be expressed as a convex combination of permutation matrices.
APA, Harvard, Vancouver, ISO, and other styles
49

MARTINS, RACHEL A. D. "NONCOMMUTATIVE FERMION MASS MATRIX AND GRAVITY." International Journal of Modern Physics A 28, no. 25 (2013): 1350120. http://dx.doi.org/10.1142/s0217751x13501200.

Full text
Abstract:
The first part is an introductory description of a small cross-section of the literature on algebraic methods in nonperturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of the nature of geometry. This helps to set the context for the second part, in which we describe a new algebraic characterization of the Dirac operator in noncommutative geometry and then use it in a calculation on the form of the fermion mass matrix. Assimilating and building on the various ideas described in the first part, the final part consists of an outline of a speculative perspective on (noncommutative) quantum spectral gravity. This is the second of a pair of papers so far on this project.
APA, Harvard, Vancouver, ISO, and other styles
50

Mairesse, Jean. "Products of Irreducible Random Matrices in the (Max, +) Algebra." Advances in Applied Probability 29, no. 02 (1997): 444–77. http://dx.doi.org/10.1017/s0001867800028081.

Full text
Abstract:
We consider the recursive equation x(n + 1)= A(n)⊗x(n), where x(n + 1) and x(n) are ℝ k -valued vectors and A(n) is an irreducible random matrix of size k × k. The matrix-vector multiplication in the (max, +) algebra is defined by (A(n)⊗x(n))= maxj (Aij (n) + xj (n)). This type of equation can be used to represent the evolution of stochastic event graphs which include cyclic Jackson networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the sequence {A(n), n ∈ ℕ} is i.i.d. or, more generally, stationary and ergodic. The main result of the paper states that the system couples in finite time with a unique stationary regime if and only if there exists a set of matrices such that and the matrices have a unique periodic regime.
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography