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Let #math12#S = [s_ij] (#math13#1≤i, j≤n) be a (0, 1, - 1)-matrix of order n. Then S is a <#40#>sign-nonsingular matrix<#40#> (SNS-matrix) provided that each real matrix with the same sign pattern as S is nonsingular. There has been considerable recent interest in constructing and characterizing SNS-matrices [#bs##1###], [#klm##1###]. There has also been interest in strong forms of sign-nonsingularity [#djd##1###]. In this paper we give a new generalization of SNS-matrices and investigate some of their basic properties.

Let #math14#S = [s_ij] be a (0, 1, - 1)-matrix of order n and let #math15#C = [c_ij] be a real matrix of order n. The pair (S, C) is called a <#46#>matrix pair of order<#46#> n. Throughout, #math16#X = [x_ij] denotes a matrix of order n whose entries are algebraically independent indeterminates over the real field. Let SoX denote the Hadamard product (entrywise product) of S and X. We say that the pair (S, C) is a <#48#>sign-nonsingular matrix pair of order<#48#> n, abbreviated SNS-<#49#>matrix pair of order<#49#> n, provided that the matrix

#math17#

A = SoX + C

is nonsingular for all positive real values of the x_ij. If C = O then the pair (S, O) is a SNS-matrix pair if and only if S is a SNS-matrix. If S = O then the pair (O, C) is a SNS-matrix pair if and only if C is nonsingular. Thus SNS-matrix pairs include both nonsingular matrices and sign-nonsingular matrices as special cases.

The pairs (S, C) with

#math18#

S = #tex2html_wrap_indisplay1208##tex2html_wrap_indisplay1209##tex2html_wrap_indisplay1210#,;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;C = #tex2html_wrap_indisplay1211##tex2html_wrap_indisplay1212##tex2html_wrap_indisplay1213#

and

#math19#

S = #tex2html_wrap_indisplay1215##tex2html_wrap_indisplay1216##tex2html_wrap_indisplay1217#,;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;;SPMnbsp;C = #tex2html_wrap_indisplay1218##tex2html_wrap_indisplay1219##tex2html_wrap_indisplay1220#

are examples of SNS-matrix pairs.