A solution to the problem of separating a regular factor from a matrix polynomial

1981 ◽  
Vol 32 (4) ◽  
pp. 332-343 ◽  
Author(s):  
P. S. Kazimirskii
Keyword(s):  
Matrix Polynomial ◽  
Regular Factor

Stability analysis of switched systems with all subsystems unstable: A matrix polynomial approach

2021 ◽  
Author(s):  
Lei Cheng ◽  
Xiaozeng Xu ◽  
Yuxi Xue ◽  
Hongbin Zhang
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Matrix Polynomial

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

Iterative vs. regular factor algebras

1983 ◽  
Vol 15 (2) ◽  
pp. 32-44 ◽  
Author(s):  
Irène Guessarian ◽  
Francesco Parisi-Presicce
Keyword(s):  
Regular Factor

scholarly journals A Schur-Cohn theorem for matrix polynomials

1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young
Keyword(s):  
Unit Circle ◽  
Matrix Polynomial ◽  
Hermitian Matrix ◽  
Krein Space ◽  
Gram Matrix ◽  
Natural Basis ◽  
Test Matrix ◽  
Matrix Polynomials ◽  
Rational Vector ◽  
Square Matrix

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.

A fast algorithm for evaluating the matrix polynomial I+A+. . .+A/sup N-1/

1992 ◽  
Vol 39 (4) ◽  
pp. 299-300 ◽  
Author(s):  
L. Lei ◽  
T. Nakamura
Keyword(s):  
Fast Algorithm ◽  
Matrix Polynomial ◽  
The Matrix

A Note on the Level Sets of a Matrix Polynomial and Its Numerical Range

2002 ◽  
pp. 277-281
Author(s):  
Panayiotis J. Psarrakos
Keyword(s):  
Level Sets ◽  
Matrix Polynomial ◽  
Numerical Range
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