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Journal articles on the topic 'Singularna matrica'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Radošević Medvidović, Ines, and Kristina Pedić. "Matrične faktorizacije." Zbornik radova 20, no. 1 (2018): 227–42. http://dx.doi.org/10.32762/zr.20.1.14.

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Matrice se dijele u različite klase, ovisno o formi i određenim svojstvima. Matrične faktorizacije ovise o svojstvima određene klase matrica pa su faktorizacije matrica od velikog značaja u teoriji matrica, pri analizi numeričkih algoritama i uopće u numeričkoj linearnoj algebri. Faktorizacija matrice A je prikaz matrice A kao produkta "jednostavnijih" matrica, što omogućuje jednostavnije rješavanje nekog problema. U teoriji matrica značajne su faktorizacije onih matrica kod kojih je moguća transformacija sličnost, kod što su Schurova dekompozicija, spektralna dekompozicija, singularna dekompo

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2

Lasserre, Jean B. "A formula for singular perturbations of Markov chains." Journal of Applied Probability 31, no. 3 (1994): 829–33. http://dx.doi.org/10.2307/3215160.

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We give formulas for updating both the steady-state probability distribution and the fundamental matrices of a singularly perturbed Markov chain. This formula generalizes Schweitzer's regular perturbation formulas to the case of singular perturbations.

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3

Lasserre, Jean B. "A formula for singular perturbations of Markov chains." Journal of Applied Probability 31, no. 03 (1994): 829–33. http://dx.doi.org/10.1017/s0021900200045381.

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We give formulas for updating both the steady-state probability distribution and the fundamental matrices of a singularly perturbed Markov chain. This formula generalizes Schweitzer's regular perturbation formulas to the case of singular perturbations.

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4

Romaniv, O. M., and A. V. Sagan. "$\omega$-Euclidean domain and Laurent series." Carpathian Mathematical Publications 8, no. 1 (2016): 158–62. http://dx.doi.org/10.15330/cmp.8.1.158-162.

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It is proved that a commutative domain $R$ is $\omega$-Euclidean if and only if the ring of formal Laurent series over $R$ is $\omega$-Euclidean domain. It is also proved that every singular matrice over ring of formal Laurent series $R_{X}$ are products of idempotent matrices if $R$ is $\omega$-Euclidean domain.

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5

Yoo, Heonjong, Zoran Gajic, and Kyeong-Hwan Lee. "Reduced-Order Algorithm for Eigenvalue Assignment of Singularly Perturbed Linear Systems." Mathematical Problems in Engineering 2020 (May 30, 2020): 1–10. http://dx.doi.org/10.1155/2020/3948564.

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In this paper, we present an algorithm for eigenvalue assignment of linear singularly perturbed systems in terms of reduced-order slow and fast subproblem matrices. No similar algorithm exists in the literature. First, we present an algorithm for the recursive solution of the singularly perturbed algebraic Sylvester equation used for eigenvalue assignment. Due to the presence of a small singular perturbation parameter that indicates separation of the system variables into slow and fast, the corresponding algebraic Sylvester equation is numerically ill-conditioned. The proposed method for the r

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6

Eskin, Alex, and Yonatan R. Katznelson. "Singular symmetric matrices." Duke Mathematical Journal 79, no. 2 (1995): 515–47. http://dx.doi.org/10.1215/s0012-7094-95-07913-7.

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7

Atkinson, David. "Singular Scattering Matrices." Journal of Nonlinear Mathematical Physics 12, sup1 (2005): 43–49. http://dx.doi.org/10.2991/jnmp.2005.12.s1.4.

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8

Gil, José J., Razvigor Ossikovski, and Ignacio San José. "Singular Mueller matrices." Journal of the Optical Society of America A 33, no. 4 (2016): 600. http://dx.doi.org/10.1364/josaa.33.000600.

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9

Lytova, A., and L. Pastur. "On a Limiting Distribution of Singular Values of Random Band Matrices." Zurnal matematiceskoj fiziki, analiza, geometrii 11, no. 4 (2015): 311–32. http://dx.doi.org/10.15407/mag11.04.311.

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10

Yakovets, V. P. "Asymptotic analysis of a singularly perturbed linear system with a singular limit pencil of matrices." Ukrainian Mathematical Journal 44, no. 1 (1992): 96–110. http://dx.doi.org/10.1007/bf01062632.

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11

Kim, In-Jae, and Bryan L. Shader. "Non-singular acyclic matrices." Linear and Multilinear Algebra 57, no. 4 (2009): 399–407. http://dx.doi.org/10.1080/03081080701823286.

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12

Sourour, A. R., and Kunikyo Tang. "Factorization of singular matrices." Proceedings of the American Mathematical Society 116, no. 3 (1992): 629. http://dx.doi.org/10.1090/s0002-9939-1992-1097352-4.

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13

Winkler, Joab R. "Singular projective transformation matrices." Applied Mathematical Modelling 20, no. 10 (1996): 771–78. http://dx.doi.org/10.1016/0307-904x(96)00081-9.

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14

Díaz-García, José A., and Ramón Gutiérrez-Jáimez. "Singular matric and matrix variate distributions." Journal of Statistical Planning and Inference 139, no. 7 (2009): 2382–87. http://dx.doi.org/10.1016/j.jspi.2008.11.001.

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15

de Seguins Pazzis, Clément. "The singular linear preservers of non-singular matrices." Linear Algebra and its Applications 433, no. 2 (2010): 483–90. http://dx.doi.org/10.1016/j.laa.2010.03.021.

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16

Berry, Michael W. "Large-Scale Sparse Singular Value Computations." International Journal of Supercomputing Applications 6, no. 1 (1992): 13–49. http://dx.doi.org/10.1177/109434209200600103.

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We present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We emphasize Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography. The target architectures for our implementations are the CRAY-2S/4–128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information

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17

Oktaba, Wiktor, and Andrzej Kieloch. "Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix." Applications of Mathematics 38, no. 1 (1993): 61–66. http://dx.doi.org/10.21136/am.1993.104534.

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18

Xue, Jianming, and Xingkai Hu. "Singular value inequalities for sector matrices." Filomat 33, no. 16 (2019): 5231–36. http://dx.doi.org/10.2298/fil1916231x.

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In this paper, we present two singular value inequalities for sector matrices. As a consequence, we prove unitarily invariant norm inequalities for sector matrices. Moreover, we present some determinant inequalities for accretive-dissipative matrices.

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19

Călugăreanu, Grigore. "Singular matrices that are products of two idempotents or products of two nilpotents." Special Matrices 10, no. 1 (2021): 47–55. http://dx.doi.org/10.1515/spma-2021-0146.

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Abstract Over commutative domains we characterize the singular 2 × 2 matrices which are products of two idempotents or products of two nilpotents. The relevant casees are the matrices with zero second row and the singular matrices with only nonzero entries.

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20

Kalauch, A., S. Lavanya, and K. C. Sivakumar. "Singular irreducible M-matrices revisited." Linear Algebra and its Applications 565 (March 2019): 47–64. http://dx.doi.org/10.1016/j.laa.2018.11.030.

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21

Brock, Kerry G. "How rare are singular matrices?" Mathematical Gazette 89, no. 516 (2004): 378–84. http://dx.doi.org/10.1017/s0025557200178210.

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Just how many matrices have inverses? In elementary linear algebra courses, many of the matrices encountered are singular, but perhaps the reason is that such matrices provide rich and interesting examples. How many of them occur naturally? Many beginning students observe that a singular matrix can be made nonsingular by very minor tweaking – changing just one entry, for example, will make a matrix of rank n – 1 into a full rank (nonsingular) matrix. In fact, changing one entry just a tiny bit will do it. Looking at the question from that point of view, with a little experimentation students b

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22

Lenders, Patrick, and Jingling Xue. "Factorization of singular integer matrices." Linear Algebra and its Applications 428, no. 4 (2008): 1046–55. http://dx.doi.org/10.1016/j.laa.2007.09.012.

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23

Rangamani, Nishant. "Singular-unbounded random Jacobi matrices." Journal of Mathematical Physics 60, no. 8 (2019): 081904. http://dx.doi.org/10.1063/1.5085027.

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24

Rokni, M., B. S. Berger, and I. Minis. "SINGULAR VALUES OF CUMULANT MATRICES." Journal of Sound and Vibration 205, no. 5 (1997): 706–11. http://dx.doi.org/10.1006/jsvi.1997.1026.

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25

Haemers, Willem H. "Conditions for Singular Incidence Matrices." Journal of Algebraic Combinatorics 21, no. 2 (2005): 179–83. http://dx.doi.org/10.1007/s10801-005-6907-z.

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26

Dai, Wei, and Yongsheng Ye. "A Characterization on Singular Value Inequalities of Matrices." Journal of Function Spaces 2020 (February 18, 2020): 1–4. http://dx.doi.org/10.1155/2020/1657381.

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We obtain a characterization of pair matrices A and B of order n such that sjA≤sjB, j=1, …, n, where sjX denotes the j-th largest singular values of X. It can imply not only some well-known singular value inequalities for sums and direct sums of matrices but also Zhan’s result related to singular values of differences of positive semidefinite matrices. In addition, some related and new inequalities are also obtained.

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27

Newton, Paul K., and Stephen A. DeSalvo. "The Shannon entropy of Sudoku matrices." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (2010): 1957–75. http://dx.doi.org/10.1098/rspa.2009.0522.

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We study properties of an ensemble of Sudoku matrices (a special type of doubly stochastic matrix when normalized) using their statistically averaged singular values. The determinants are very nearly Cauchy distributed about the origin. The largest singular value is , while the others decrease approximately linearly. The normalized singular values (obtained by dividing each singular value by the sum of all nine singular values) are then used to calculate the average Shannon entropy of the ensemble, a measure of the distribution of ‘energy’ among the singular modes and interpreted as a measure

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28

Journal, Baghdad Science. "New Formulas of Special Singular Matrices." Baghdad Science Journal 6, no. 2 (2009): 405–9. http://dx.doi.org/10.21123/bsj.6.2.405-409.

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Many of the elementary transformations of determinants which are used in their evaluation and in the solution of linear equations may by expressed in the notation of matrices. In this paper, some new interesting formulas of special matrices are introduced and proved that the determinants of these special matrices have the values zero. All formulation has been coded in MATLAB 7.

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29

Corr, Brian P., Tomasz Popiel, and Cheryl E. Praeger. "Nilpotent-independent sets and estimation in matrix algebras." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 404–18. http://dx.doi.org/10.1112/s146115701500008x.

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Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for such algorithms require knowledge of the proportion of relevant matrices in the ambient group or algebra. We introduce a method for estimating proportions of families $N$ of elements in the algebra of all $d\times d$ matrices over a field of order $q$, where membership of a matrix in $N$ depends only on its ‘invertible part’. The method is based on the availability of estimates for proporti

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30

Gao, You, and Xiaojuan Zhang. "Constructions of compressed sensing matrices based on the subspaces of symplectic space over finite fields." Journal of Algebra and Its Applications 15, no. 02 (2015): 1650025. http://dx.doi.org/10.1142/s0219498816500250.

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The paper provides two constructions of compressed sensing matrices using the subspaces of symplectic space and singular symplectic space over finite fields. Then we compare the matrices constructed in this paper with the matrix constructed by DeVore, and compare the two matrices based on symplectic geometry and singular symplectic geometry over finite fields.

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31

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.

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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 Gersgori

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32

NIV, ADI. "FACTORIZATION OF TROPICAL MATRICES." Journal of Algebra and Its Applications 13, no. 01 (2013): 1350066. http://dx.doi.org/10.1142/s0219498813500667.

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In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We do prove the factorizability of any tropically non-singular 2 × 2 matrix and, relating to the existing Bruhat decomposition, determine which 3 × 3 matrices are factorizable. Nevertheless, there is a closure operation, obtained by means of the tropical adjoint, which is always factorizable, generalizing the decomposition of the closure operation * of a matrix.

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33

Ding, Xiucai. "Singular vector distribution of sample covariance matrices." Advances in Applied Probability 51, no. 01 (2019): 236–67. http://dx.doi.org/10.1017/apr.2019.10.

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AbstractWe consider a class of sample covariance matrices of the form Q = TXX*T*, where X = (xij) is an M×N rectangular matrix consisting of independent and identically distributed entries, and T is a deterministic matrix such that T*T is diagonal. Assuming that M is comparable to N, we prove that the distribution of the components of the right singular vectors close to the edge singular values agrees with that of Gaussian ensembles provided the first two moments of xij coincide with the Gaussian random variables. For the right singular vectors associated with the bulk singular values, the sam

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34

Li, Wei, and Keshav Pingali. "A singular loop transformation framework based on non-singular matrices." International Journal of Parallel Programming 22, no. 2 (1994): 183–205. http://dx.doi.org/10.1007/bf02577874.

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35

CLARK, SEAN, CHI-KWONG LI, and ASHWIN RASTOGI. "SCHUR MULTIPLICATIVE MAPS ON MATRICES." Bulletin of the Australian Mathematical Society 77, no. 1 (2008): 49–72. http://dx.doi.org/10.1017/s0004972708000051.

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AbstractThe structure of Schur multiplicative maps on matrices over a field is studied. The result is then used to characterize Schur multiplicative maps f satisfying $f(S) \subseteq S$ for different subsets S of matrices including the set of rank k matrices, the set of singular matrices, and the set of invertible matrices. Characterizations are also obtained for maps on matrices such that Γ(f(A))=Γ(A) for various functions Γ including the rank function, the determinant function, and the elementary symmetric functions of the eigenvalues. These results include analogs of the theorems of Frobeni

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36

Jeyaraman, I., and K. C. Sivakumar. "Complementarity properties of singular M-matrices." Linear Algebra and its Applications 510 (December 2016): 42–63. http://dx.doi.org/10.1016/j.laa.2016.08.003.

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37

Demmel, James, and W. Kahan. "Accurate Singular Values of Bidiagonal Matrices." SIAM Journal on Scientific and Statistical Computing 11, no. 5 (1990): 873–912. http://dx.doi.org/10.1137/0911052.

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38

Li, Wen. "Characterizations of singular irreducible M-matrices." Linear and Multilinear Algebra 38, no. 3 (1995): 241–47. http://dx.doi.org/10.1080/03081089508818360.

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39

Buoni, J. J. "Incomplete Factorization of Singular M-Matrices." SIAM Journal on Algebraic Discrete Methods 7, no. 2 (1986): 193–98. http://dx.doi.org/10.1137/0607023.

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40

Alahmadi, Adel, S. K. Jain, and André Leroy. "Decomposition of singular matrices into idempotents." Linear and Multilinear Algebra 62, no. 1 (2013): 13–27. http://dx.doi.org/10.1080/03081087.2012.754439.

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41

Hilberdink, Titus. "Singular values of multiplicative Toeplitz matrices." Linear and Multilinear Algebra 65, no. 4 (2016): 813–29. http://dx.doi.org/10.1080/03081087.2016.1204978.

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42

BAZÁN, F. S. V., and Ph L. TOINT. "SINGULAR VALUE ANALYSIS OF PREDICTOR MATRICES." Mechanical Systems and Signal Processing 15, no. 4 (2001): 667–83. http://dx.doi.org/10.1006/mssp.2000.1370.

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43

Duffner, M. A., and A. E. Guterman. "Converting immanants on singular symmetric matrices." Lobachevskii Journal of Mathematics 38, no. 4 (2017): 630–36. http://dx.doi.org/10.1134/s1995080217040060.

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44

Greenacre, Michael. "Singular value decomposition of matched matrices." Journal of Applied Statistics 30, no. 10 (2003): 1101–13. http://dx.doi.org/10.1080/0266476032000107132.

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45

Anderson, Brian D. O., Manfred Deistler, Weitian Chen, and Alexander Filler. "Autoregressive models of singular spectral matrices." Automatica 48, no. 11 (2012): 2843–49. http://dx.doi.org/10.1016/j.automatica.2012.05.047.

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46

Tyrtyshnikov, Evgenij E. "Singular values of cauchy-toeplitz matrices." Linear Algebra and its Applications 161 (January 1992): 99–116. http://dx.doi.org/10.1016/0024-3795(92)90007-w.

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47

Ratnarajah, T., and R. Vaillancourt. "Complex singular wishart matrices and applications." Computers & Mathematics with Applications 50, no. 3-4 (2005): 399–411. http://dx.doi.org/10.1016/j.camwa.2005.04.009.

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48

Jódar, Lucas, and Enrique Navarro. "Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems." Applications of Mathematics 39, no. 3 (1994): 189–202. http://dx.doi.org/10.21136/am.1994.134252.

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49

Rehman, Mutti-Ur, Jehad Alzabut, Javed Hussain Brohi, and Arfan Hyder. "On Spectral Properties of Doubly Stochastic Matrices." Symmetry 12, no. 3 (2020): 369. http://dx.doi.org/10.3390/sym12030369.

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The relationship among eigenvalues, singular values, and quadratic forms associated with linear transforms of doubly stochastic matrices has remained an important topic since 1949. The main objective of this article is to present some useful theorems, concerning the spectral properties of doubly stochastic matrices. The computation of the bounds of structured singular values for a family of doubly stochastic matrices is presented by using low-rank ordinary differential equations-based techniques. The numerical computations illustrating the behavior of the method and the spectrum of doubly stoc

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50

Ciliz, M. K., and H. Krishna. "Split Levinson algorithm for Toeplitz matrices with singular sub-matrices." IEEE Transactions on Circuits and Systems 36, no. 6 (1989): 922–24. http://dx.doi.org/10.1109/31.90420.

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