scholarly journals On Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography

2013 ◽  
pp. 29-43 ◽  
Author(s):  
Kishan Chand Gupta ◽  
Indranil Ghosh Ray
Keyword(s):  
Lightweight Cryptography ◽  
Companion Matrices

scholarly journals Toeplitz nonnegative realization of spectra via companion matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Half Plane ◽  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Nonnegative Matrix ◽  
Inverse Eigenvalue Problem ◽  
Complex Numbers ◽  
Inverse Eigenvalue ◽  
Companion Matrices ◽  
Solution Matrix

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}. If the problem has a solution, we say that Λ is realizable and that A is a realizing matrix. In this paper we consider the NIEP for a Toeplitz realizing matrix A, and as far as we know, this is the first work which addresses the Toeplitz nonnegative realization of spectra. We show that nonnegative companion matrices are similar to nonnegative Toeplitz ones. We note that, as a consequence, a realizable list Λ= {λ1, . . ., λn} of complex numbers in the left-half plane, that is, with Re λi≤ 0, i = 2, . . ., n, is in particular realizable by a Toeplitz matrix. Moreover, we show how to construct symmetric nonnegative block Toeplitz matrices with prescribed spectrum and we explore the universal realizability of lists, which are realizable by this kind of matrices. We also propose a Matlab Toeplitz routine to compute a Toeplitz solution matrix.

scholarly journals Bounds on polynomial roots using intercyclic companion matrices

2018 ◽  
Vol 539 ◽  
pp. 94-116
Author(s):  
Kevin N. Vander Meulen ◽  
Trevor Vanderwoerd
Keyword(s):  
Polynomial Roots ◽  
Companion Matrices

scholarly journals Three-way companion matrices of three-variable polynomials

1981 ◽  
Vol 37 ◽  
pp. 55-75 ◽  
Author(s):  
Krzysztof Gałlkowski
Keyword(s):  
Companion Matrices

A noncommutative spectral theorem for operator entried companion matrices

1981 ◽  
Vol 10 (1) ◽  
pp. 45-51
Author(s):  
John de Pillis ◽  
Michael Neumann
Keyword(s):  
Spectral Theorem ◽  
Companion Matrices
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