Abstract

A real, square matrix with nonpositive off-diagonal elements is a Z-matrix, and a Z-matrix with nonnegative principal minors is an M-matrix. Using principal pivoting, we derive a polynomial-time algorithm for testing whether a Z-matrix is an M-matrix. Our algorithm is much simpler than a recent one proposed by Ramamurthy. We also study the zero-nonzero structure of the inverse of a nonsingular M-matrix and compare A -1 and B -1 in the case that A and B are nonsingular M-matrices and B ≧ A.

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