Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the nonsingularity of real matrices


Author: A. J. Hoffman
Journal: Math. Comp. 19 (1965), 56-61
MSC: Primary 15.25; Secondary 15.20
MathSciNet review: 0174566
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 15.25, 15.20

Retrieve articles in all journals with MSC: 15.25, 15.20


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1965-0174566-0
PII: S 0025-5718(1965)0174566-0
Article copyright: © Copyright 1965 American Mathematical Society