Results 1 to 10 of about 48,136 (148)
On Characteristic Polynomial of Antiadjacency Matrix of A Line Digraph
Jurnal Matematika UNAND, 2022 In this paper, we find the characteristic polynomial of the antiadjacency matrix of a line digraph. There are recent studies on the relation between the characteristic polynomial of the adjacency matrix and its line digraph, we are also interested in ...
Muhammad Irfan Arsyad Prayitno +1 more
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Hermitian and Unitary Almost-Companion Matrices of Polynomials on Demand
Entropy, 2023 We introduce the concept of the almost-companion matrix (ACM) by relaxing the non-derogatory property of the standard companion matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and generally ...
Liubov A. Markovich +2 more
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Matrix approach to solve polynomial equations
Results in Applied Mathematics, 2023 Polynomials are widely employed to represent numbers derived from mathematical operations in nearly all areas of mathematics. The ability to factor polynomials entirely into linear components allows for a wide range of problem simplifications. This paper
Samir Brahim Belhaouari +2 more
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Triangularizing Quadratic Matrix Polynomials [PDF]
SIAM Journal on Matrix Analysis and Applications, 2013 We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable ...
Tisseur, Françoise, Zaballa, Ion
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IET Control Theory & Applications, 2023 The problem of the singular Roesser (state‐space) model realization of non‐causal multivariate transfer (function) matrices is investigated. Specifically, the notion of so‐called admissible transformation is introduced, which allows to introduce and ...
Dongdong Zhao +5 more
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Efficient Evaluation of Matrix Polynomials beyond the Paterson–Stockmeyer Method
Mathematics, 2021 Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson–Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matrix ...
Jorge Sastre, Javier Ibáñez
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Stieltjes Property of Quasi-Stable Matrix Polynomials
Mathematics, 2022 In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built ...
Xuzhou Zhan, Bohui Ban, Yongjian Hu
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Matrix Approaches for Gould–Hopper–Laguerre–Sheffer Matrix Polynomial Identities
Axioms, 2023 The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques.
Tabinda Nahid +2 more
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CHARACTERISTIC ANTIADJACENCY MATRIX OF GRAPH JOIN
Barekeng, 2022 Let be a simple, connected, and undirected graph. The graph can be represented as a matrix such as antiadjacency matrix. An antiadjacency matrix for an undirected graph with order is a matrix that has an order and symmetric so that the ...
Wahri Irawan, Kiki Ariyanti Sugeng
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Matrix-Valued Gegenbauer-Type Polynomials [PDF]
Constructive Approximation, 2017 Matrix-valued Gegenbauer-type polynomials are investigated. The main results of the paper are stated in Sections 2 and 3. In Section 2 the matrix-valued weight functions \(W^{(\nu)}(x)\), which are analogues of the weight function for the Gegenbauer polynomials \(C^{(\nu)}_n(x)\) are introduced: \(W^{(\nu)}(x)= (1-x^2)^{\nu-1/2}W^{(\nu)}_{\mathrm{pol}}(
Koelink, Erik +2 more
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