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Academic literature on the topic 'Polynomial matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Polynomial matrices"

1

Chami, Peter S., Bernd Sing, and Norris Sookoo. "Generalizing Krawtchouk Polynomials Using Hadamard Matrices." ISRN Applied Mathematics 2014 (March 4, 2014): 1–8. http://dx.doi.org/10.1155/2014/498135.

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We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged in a square matrix; in particular, the case where this matrix is a Hadamard matrix is considered. Orthogonality relations and recurrence relations are established, and coefficients for the expansion of any polynomial in terms of m-polynomials are obtained. We conclude this paper by an implementation of m-polynomials and some of the results obtained for them in Mathematica.

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Akemann, Gernot, Eugene Strahov, and Tim R. Würfel. "Averages of Products and Ratios of Characteristic Polynomials in Polynomial Ensembles." Annales Henri Poincaré 21, no. 12 (2020): 3973–4002. http://dx.doi.org/10.1007/s00023-020-00963-9.

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Abstract Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external field, that may serve as schematic models of quantum field theories with temperature. We first analyse expectation values of ratios of an equal number of characteristic polynomials in general polynomial ensembles. Using Schur polynomials, we show that polynomial ensembles constitute Giambelli compatible point processes, leading to a determinant formula f

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Shavarovskii, B. Z. "Factorable polynomial matrices." Mathematical Notes 68, no. 4 (2000): 507–18. http://dx.doi.org/10.1007/bf02676732.

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Hudelson, Matt, Judi McDonald, and Enzo Wendler. "Alpha Adjacency: A generalization of adjacency matrices." Electronic Journal of Linear Algebra 35 (February 1, 2019): 365–75. http://dx.doi.org/10.13001/1081-3810.3828.

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B. Shader and W. So introduced the idea of the skew adjacency matrix. Their idea was to give an orientation to a simple undirected graph G from which a skew adjacency matrix S(G) is created. The -adjacency matrix extends this idea to an arbitrary field F. To study the underlying undirected graph, the average -characteristic polynomial can be created by averaging the characteristic polynomials over all the possible orientations. In particular, a Harary-Sachs theorem for the average-characteristic polynomial is derived and used to determine a few features of the graph from the average-characteri

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Seneta, E. "Characterization by orthogonal polynomial systems of finite Markov chains." Journal of Applied Probability 38, A (2001): 42–52. http://dx.doi.org/10.1017/s0021900200112665.

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The paper characterizes matriceswhich have a given system of vectors orthogonal with respect to a given probability distribution as its right eigenvectors. Results of Hoare and Rahman are unified in this context, then all matrices with a given orthogonal polynomial system as right eigenvectors under the constrainta0j= 0 forj≥ 2 are specified. The only stochastic matricesP ={pij} satisfyingp00+p01= 1 with the Hahn polynomials as right eigenvectors have the form of the Moran mutation model.

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Ramesh, G., and R. Gajalakshmi. "On Orthogonal Polynomial Matrices." IOSR Journal of Mathematics 13, no. 02 (2017): 33–37. http://dx.doi.org/10.9790/5728-1302043337.

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Zhou, Guangcai, and Xiang-Gen Xia. "Ambiguity resistant polynomial matrices." Linear Algebra and its Applications 286, no. 1-3 (1999): 19–35. http://dx.doi.org/10.1016/s0024-3795(98)10127-1.

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Pierce, Stephen. "Congruence of polynomial matrices." Linear Algebra and its Applications 294, no. 1-3 (1999): 1–8. http://dx.doi.org/10.1016/s0024-3795(99)00029-4.

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Eising, R. "Polynomial matrices and feedback." IEEE Transactions on Automatic Control 30, no. 10 (1985): 1022–25. http://dx.doi.org/10.1109/tac.1985.1103829.

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Qing-Guo Wang, Chun-Hui Zhou, and You-Xian Sun. "Stability of polynomial matrices." IEEE Transactions on Automatic Control 32, no. 3 (1987): 228. http://dx.doi.org/10.1109/tac.1987.1104571.

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Dissertations / Theses on the topic "Polynomial matrices"

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Dale, Hill Jordan. "Polynomial identities for skew-symmetric matrices." Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/27347.

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As mentioned in the introduction, Racine and D'Amour have described all identities for Kn, n < 5. In our research we began at n = 5, and immediately found that 8 is the minimal degree, and that there is a large space of identities for degree 8. More precisely, a space of degree 8 multilinear identities for K5 was computed and it has dimension 1756. A character for this space was also computed and it involves, in its decomposition into irreducible characters, all but 4 of S8's irreducible characters. Our next step was to look into this massive space for "simple" identities: identities that m

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Adamsson, Jay M. H. "The standard polynomial as an identity on symplectic matrices." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7525.

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The symplectic involution s is defined on $2n \times 2n$ matrices by $$\pmatrix{A&B\cr C&D\cr}\sp{s} = \pmatrix{D\sp{t}&-B\sp{t}\cr -C\sp{t}&A\sp{t}\cr}$$ where A, B, C, and D are $n\times n$ matrices, and t is the standard transpose operation. This thesis investigates the value of the standard polynomial $S\sb{k} := \sum\sb{\sigma\in{\cal S}\sb{k}} (-1)\sp{\sigma} x\sb{\sigma(1)}\cdots x\sb{\sigma(k)}$ evaluated over the ring of matrices which are symmetric with respect to the symplectic involution, denoted $H\sb{n}(F, s).$ In this thesis the value of $S\sb{4n-3}$ for $n \ge 3$ is studied. In

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Johnson, Dean S. "Coprimeness in multidimensional system theory and symbolic computation." Thesis, Loughborough University, 1993. https://dspace.lboro.ac.uk/2134/31933.

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During the last twenty years the theory of linear algebraic and high-order differential equation systems has been greatly researched. Two commonly used types of system description are the so-called matrix fraction description (MFD) and the Rosenbrock system matrix (RSM); these are defined by polynomial matrices in one indeterminate. Many of the system's physical properties are encoded as algebraic properties of these polynomial matrices. The theory is well developed and the structure of such systems is well understood. Analogues of these 1-D realisations can be set up for many dimensional syst

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Cheng, Howard. "Algorithms for Normal Forms for Matrices of Polynomials and Ore Polynomials." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1088.

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In this thesis we study algorithms for computing normal forms for matrices of Ore polynomials while controlling coefficient growth. By formulating row reduction as a linear algebra problem, we obtain a fraction-free algorithm for row reduction for matrices of Ore polynomials. The algorithm allows us to compute the rank and a basis of the left nullspace of the input matrix. When the input is restricted to matrices of shift polynomials and ordinary polynomials, we obtain fraction-free algorithms for computing row-reduced forms and weak Popov forms. These algorithms can be used to com

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Oliveira, Júnior Pedro Jerônimo Simões de. "Equações polinomiais e matrizes circulantes." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9344.

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Maurice, Rémi. "Algèbres de Hopf combinatoires." Thesis, Paris Est, 2013. http://www.theses.fr/2013PEST1196/document.

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Cette thèse se situe dans le domaine de la combinatoire algébrique. Autrement dit, l'idée est d'utiliser des structures algébriques, en l'occurence des algèbres de Hopf combinatoires, pour mieux étudier et comprendre les objets combinatoires ainsi que des algorithmes de composition et de décomposition agissant sur ces objets. Ce travail de recherche repose sur la construction et l'étude de structure algébrique sur des objets combinatoires généralisant les permutations. Après avoir rappelé le contexte et les notations des différents objets intervenant dans cette recherche, nous proposons dans l

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McInerney, Simon J. "Representations and transformations for multi-dimensional systems." Thesis, Loughborough University, 1999. https://dspace.lboro.ac.uk/2134/28237.

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Multi-dimensional (n-D) systems can be described by matrices whose elements are polynomial in more than one indeterminate. These systems arise in the study of partial differential equations and delay differential equations for example, and have attracted great interest over recent years. Many of the available results have been developed by generalising the corresponding results from the well known 1-D theory. However, this is not always the best approach since there are many differences between 1-D, 2-D and n-D (n > 2) polynomial matrices. This is due mainly to the underlying polynomial ring s

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Lahnovych, Carrie. "Analysis and computation of a quadratic matrix polynomial with Schur-products and applications to the Barboy-Tenne model /." Online version of thesis, 2010. http://ritdml.rit.edu/handle/1850/12207.

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Davidson, Colin. "Reductions and Triangularizations of Sets of Matrices." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2918.

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Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in finite dimensional and infinite dimensional Banach spaces. In addition, we investigate whether approximate spectral mapping conditions (being "close" in some sense) is similarly a sufficient condition.

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Lee, Sang-Gu. "Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings." DigitalCommons@USU, 1991. https://digitalcommons.usu.edu/etd/6984.

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We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = Xr1 + Xr2 + ... + Xrt and r1>r2>...>rt≥2. In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We also extended the

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Books on the topic "Polynomial matrices"

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Kaczorek, Tadeusz. Polynomial and Rational Matrices. Springer London, 2007. http://dx.doi.org/10.1007/978-1-84628-605-6.

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Stefanidis, Peter, Andrzej Piotr Paplińnski, and Michael John Gibbard, eds. Numerical Operations with Polynomial Matrices. Springer-Verlag, 1992. http://dx.doi.org/10.1007/bfb0039323.

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Freund, Roland W. On polynomial preconditioning for indefinite Hermitian matrices. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Victor, Pan, ed. Polynomial and matrix computations. Birkhäuser, 1994.

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1920-, Gregory Robert Todd, ed. Error-free polynomial matrix computations. Springer-Verlag, 1985.

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6

Formanek, Edward. The polynomial identities and invariants of nxn matrices. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1991.

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Formanek, Edward. The polynomial identities and invariants of n x n matrices. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1991.

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8

Fischer, Bernd. On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1992.

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9

Rawlins, A. D. A note on polynomial diagonalization and Wiener-Hopf factorization of 2x2 matrices. Brunel University, Department of Mathematics and Statistics, 1989.

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1942-, Papliński A. P., and Gibbard M. J. 1937-, eds. Numerical operations with polynomial matrices: Application to multi-variable dynamic compensator design. Springer-Verlag, 1992.

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Book chapters on the topic "Polynomial matrices"

1

Rosenwasser, Efim N., Bernhard P. Lampe, and Torsten Jeinsch. "Polynomial Matrices." In Computer-Controlled Systems with Delay. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15042-6_1.

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Falb, Peter. "Polynomial Matrices." In Methods of Algebraic Geometry in Control Theory: Part II. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96574-1_4.

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Falb, Peter. "Polynomial Matrices." In Methods of Algebraic Geometry in Control Theory: Part II. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1564-6_5.

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Drensky, Vesselin, and Edward Formanek. "Central Polynomials for Matrices." In Polynomial Identity Rings. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7934-7_5.

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Drensky, Vesselin, and Edward Formanek. "Invariant Theory of Matrices." In Polynomial Identity Rings. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7934-7_6.

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Drensky, Vesselin, and Edward Formanek. "The Ring of Generic Matrices." In Polynomial Identity Rings. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7934-7_23.

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Edwards, Harold M. "Matrices with Polynomial Entries." In Linear Algebra. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-0-8176-4446-8_8.

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Pan, Victor Y. "Toeplitz/Hankel Matrix Structure and Polynomial Computations." In Structured Matrices and Polynomials. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0129-8_2.

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Gaubert, Stéphane, and Meisam Sharify. "Tropical Scaling of Polynomial Matrices." In Positive Systems. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02894-6_28.

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Kraus, F. J., M. Mansour, and M. Sebek. "Hurwitz Matrix for Polynomial Matrices." In Stability Theory. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9208-7_8.

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Conference papers on the topic "Polynomial matrices"

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Karcanias, Nicos, and George Halikias. "Approximate zero polynomials of polynomial matrices and linear systems." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6160302.

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Corless, Robert M. "Pseudospectra for exponential polynomial matrices." In the 2009 conference. ACM Press, 2009. http://dx.doi.org/10.1145/1577190.1577192.

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Zhou, Wei, and George Labahn. "Unimodular completion of polynomial matrices." In the 39th International Symposium. ACM Press, 2014. http://dx.doi.org/10.1145/2608628.2608640.

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Long Wang, Zhizhen Wang, and Wensheng Yu. "Stability of polytopic polynomial matrices." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.945722.

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Sunkari, Rajesh Pavan, and Linda C. Schmidt. "Laplace and Extended Adjacency Matrices for Isomorphism Detection of Kinematic Chains Using the Characteristic Polynomial Approach." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84609.

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The kinematic chain isomorphism problem is one of the most challenging problems facing mechanism researchers. Methods using the spectral properties, characteristic polynomial and eigenvectors, of the graph related matrices were developed in literature for isomorphism detection. Detection of isomorphism using only the spectral properties corresponds to a polynomial time isomorphism detection algorithm. However, most of the methods used are either computationally inefficient or unreliable (i.e., failing to identify non-isomorphic chains). This work establishes the reliability of using the charac

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Zhou, Wei, and George Labahn. "Computing column bases of polynomial matrices." In the 38th international symposium. ACM Press, 2013. http://dx.doi.org/10.1145/2465506.2465947.

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Bernardi, Alessandra, Jérôme Brachat, Pierre Comon, and Bernard Mourrain. "Multihomogeneous polynomial decomposition using moment matrices." In the 36th international symposium. ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993898.

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Gupta, Somit, and Arne Storjohann. "Computing hermite forms of polynomial matrices." In the 36th international symposium. ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993913.

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Kolhekar, Megha, and Harish K. Pillai. "Permutation Polynomial Representatives and their Matrices." In 2018 Twenty Fourth National Conference on Communications (NCC). IEEE, 2018. http://dx.doi.org/10.1109/ncc.2018.8599882.

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Zerz, Eva. "Primeness of multivariate Laurent polynomial matrices." In 1997 European Control Conference (ECC). IEEE, 1997. http://dx.doi.org/10.23919/ecc.1997.7082222.

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Reports on the topic "Polynomial matrices"

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Conforti, Michele, Gerard Cornuejols, and M. R. Rao. Decomposition of Balanced Matrices. Part 7. A Polynomial Recognition Algorithm. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada247400.

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Delyon, B. Expansions for Determinants and for Characteristics Polynomials of Stochastic Matrices. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada458571.

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Saydy, Lahcen, Andre Tits, and Eyad H. Abed. Guardian Maps and the Generalized Stability of Parametrized Families of Matrices and Polynomials. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada454727.

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Tal-Ezer, Hillel. Polynominal Approximation of Functions of Matrices and Its Application the the Solution of a General System of Linear Equations. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada211390.

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