On the nonsingularity of complex matrices

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 = (bij) of order n such that, for all i, j, |bij| = aij. 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. © 1966 by Pacific Journal of Mathematics.