On the nonsingularity of real matrices-Reference-Cited by-同舟云学术

On the nonsingularity of real matrices

Published:1965 Issue:89 Volume:19 Page:56-61
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Hoffman A. J.

Abstract

By exploiting the theory of linear inequalities, new bounds for the real eigenvalues of a real matrix are derived, along with sufficient conditions for matrix games to be completely mixed, for determinants to be positive, etc. The simple observation on which the derivation of new results and the unification of old results are based is that the typical conditions of diagonal dominance which insure the nonsingularity of matrices are essentially systems of linear inequalities on the rows of the matrices.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1965-19-089/S0025-5718-1965-0174566-0/S0025-5718-1965-0174566-0.pdf

Reference4 articles.

1. Solutions of discrete, two-person games;Bohnenblust, H. F.,1950

2. Recognition of completely mixed games;Goldman, A. J.;J. Res. Nat. Bur. Standards Sect. B,1963

3. L. Negrescu, A. Németh & T. Rus, "Sur les solutions positives d’un systeme d’équations linéaires," Mathematica (Cluj), v. 4 (27), 1962, p. 65–69.

4. A recurring theorem on determinants;Taussky, Olga;Amer. Math. Monthly,1949

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