Results 21 to 30 of about 549,018 (333)
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
doaj +1 more source
Joint Numerical Range of Matrix Polynomials [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2009 Some algebraic properties of the sharp points of the joint numerical range of a matrix polynomials are the main subject of this paper. We also consider isolated points of the joint numerical range of matrix polynomials.
Ahmed Sabir
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +4 more sources
Asymptotically fast polynomial matrix algorithms for multivariable systems [PDF]
, 2005 We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer algebra techniques,
Gilles Villard +5 more
core +4 more sources
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
doaj +1 more source
Correlation kernels for sums and products of random matrices [PDF]
, 2015 Let $X$ be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared singular values of $GX$ and $TX$, where $G$ is a complex Ginibre matrix and $T$
Claeys, Tom +2 more
core +3 more sources
IEEE Access, 2020 In this paper, new conditions of the stability, stabilization and L2-gain performance of periodic piecewise systems are proposed. Both the continuous and discontinuous Lyapunov functions with dwell-time related time-varying Lyapunov matrix polynomial are
Panshuo Li +3 more
doaj +1 more source
Shortening the order of paraunitary matrices in SBR2 algorithm [PDF]
, 2007 The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the ...
Ta, C.H., Weiss, S.
core +1 more source