On the nonsingularity of real matrices

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. TBf 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 rowsof the matrices. © 1965 American Mathematical Society.