Combined matrices of sign regular matrices

Bru, Rafael; Gassó, María T.; Giménez, Isabel; Santana, Máximo

doi:10.1016/j.laa.2014.12.010

Cited by 5 publications

(7 citation statements)

References 10 publications

(14 reference statements)

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“…Sign regular matrices appear to be the natural generalization of totally positive or negative matrices and they have been a lot of attention by different authors (see in [9] and the references therein). Results of combined matrices of sign regular matrices are given in [3] and more recently in [1].…”

Section: Preliminaries and Notationmentioning

confidence: 99%

Diagonal entries of the combined matrix of sign regular matrices of order three

Gassó

Gil

Giménez

et al. 2021

Proyecciones (Antofagasta)

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The study of the diagonal entries of the combined matrix of a nonsingular matrix A has been considered by different authors for the classes of M—matrices, positive definite matrices and totally positive (negative) matrices. This problem appears to be difficult as the results have been done only for matrices of order three. In this work, we continue to give the characterization of the diagonal entries of the combined matrix of the remainder sign regular matrices. Thus, the problem is closed for all possible sign regular matrices of order three.

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Section: Preliminaries and Notationmentioning

confidence: 99%

Diagonal entries of the combined matrix of sign regular matrices of order three

Gassó

Gil

Giménez

et al. 2021

Proyecciones (Antofagasta)

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“…In the results of [6], for a SR matrix A, it is required as a hypothesis that C (A) ≥ 0 or it is proved that C (A) is not nonnegative.…”

Section: Sr Matrices With Sr Combined Matrix and Related Examplesmentioning

confidence: 99%

“…In recent years, several studies about combined matrices have been carried out (see [5][6][7][8]). In particular, in [5,6], the authors study some kinds of matrices such that their combined matrices are nonnegative, analyzing their relationship with the zero pattern of A. In this case, that is, when C (A) is nonnegative, the combined matrix is doubly stochastic.…”

Section: Introductionmentioning

confidence: 99%

Combined matrices of almost strictly sign regular matrices

Alonso

Peña

Serrano

2019

Journal of Computational and Applied Mathematics

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The combined matrix is a very useful concept for many applications. Almost strictly sign regular (ASSR) matrices form an important structured class of matrices with two possible zero patterns, which are either type-I staircase or type-II staircase. We prove that, under an irreducibility condition, the pattern of zero and nonzero entries of an ASSR matrix is preserved by the corresponding combined matrix. Without the irreducibility condition, it is proved that type-I and type-II staircases are still preserved. Illustrative numerical examples are included.

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“…Let us recall the basic definitions and properties. Some recent works on combined matrices are given in [3] for positive and negative matrices, in [4] for sign regular matrices and in [5] for H-matrices. Test to recognize total positive matrices has been studied in [15].…”

Section: Preliminariesmentioning

confidence: 99%

Diagonal entries of the combined matrix of a totally negative matrix

Bru

Gassó

Giménez

et al. 2016

Linear and Multilinear Algebra

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The combined matrix of a nonsingular matrix A is the Hadamard (entrywise) product A • A −1 T . This paper deals with the characterization of the diagonal entries of a combined matrix C(A) of a given nonsingular real matrix A. A partial answer describing the diagonal entries of C(A) in the positive definite case was given by Fiedler in 1964. Recently in 2011, Fiedler and Markham characterized the sequence of diagonal entries of the combined matrix C(A) for any totally positive matrix A when the size is 3. For this case, we characterize totally negative matrices and we find necessary and sufficient conditions for the sequence of diagonal entries of C(A), in both cases, symmetric and nonsymmetric.

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Combined matrices of sign regular matrices

Cited by 5 publications

References 10 publications

Diagonal entries of the combined matrix of sign regular matrices of order three

Diagonal entries of the combined matrix of sign regular matrices of order three

Combined matrices of almost strictly sign regular matrices

Diagonal entries of the combined matrix of a totally negative matrix

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