There are several well-known necessary and sufficient conditions for an M-matrix to possess “property c”. Specializing some of these statements, the objective here is to characterize matrices that belong to the subclass of M-matrices with “property c”, namely, singular irreducible M-matrices. A new characterization for an M-matrix A to have “property c” is given in terms of a condition involving Z-matrices C such that A≤C. A result of Fan on M-matrices is improved, and extensions to M-matrices with “property c” and singular irreducible M-matrices, are obtained. © 2018 Elsevier Inc.

K C Sivakumar

Department of Mathematics

Linear algebra

Mathematical techniques

M-matrices

Non negatives

Z MATRIX

Matrix algebra

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IIT Madras

Linear Algebra and Its Applications

In the literature on nonnegative matrix theory, real square invertible matrices with the property that their inverses are M-matrices have been extensively studied. Real square (group invertible) singular M-matrices whose group inverses are M-matrices also have received a lot of attention. The endeavour of the present work is to study the more general class of all group invertible matrices (not necessarily singular M-matrices) whose group inverses are M-matrices. Among other things, a characterization is proved. Many results, motivated by the corresponding ones for inverse M-matrices, are obtained. Let A be any 2×2 matrix or a 3×3 symmetric, tridiagonal matrix. A complete characterization for A to posses the property that its group inverse is an M-matrix, is presented. © 2019 Elsevier Inc.

Matrices whose group inverses are M-matrices

For a matrix A whose off-diagonal entries are nonpositive, its nonnegative invertibility (namely, that A is an invertible M-matrix) is equivalent to A being a P-matrix, which is necessary and sufficient for the unique solvability of the linear complementarity problem defined by A. This, in turn, is equivalent to the statement that A is strictly semimonotone. In this paper, an analogue of this result is proved for singular symmetric Z-matrices. This is achieved by replacing the inverse of A by the group generalized inverse and by introducing the matrix classes of strictly range semimonotonicity and range column sufficiency. A recently proposed idea of P#-matrices plays a pivotal role. Some interconnections between these matrix classes are also obtained. © 2016 Elsevier Inc.

Fulltext

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Singular irreducible M-matrices revisited

Journal	Data powered by TypesetLinear Algebra and Its Applications
Publisher	Data powered by TypesetElsevier Inc.
ISSN	00243795
Open Access	No