On the nonsingularity of complex matrices

Abstract

Let A -(aij) be a real square matrix of order n with nonnegative entries, and let M(A) be the class of all complex matrices B = (6^) of order n such that, for all i, j, 1b i3 [ = a i3 . If every matrix in M(A) is nonsingular, we say M(A) is regular, and it is the purpose of this note to investigate conditions under which M(A) is regular.