Some notes on Z-matrices

AbstractAn inequality is obtained relating the eigenvalue of minimum modulus of an N0-matrix A to the eigenvalue of minimum modulus of (A⧸A11)—the Schur complement of A11 in A—where A11 is an M-matrix. Similar results are obtained for irreducible M-matrices and irreducible nonsingular F0-matrices. Circulant N0-matrices of order three are characterized in terms of their spectrum. Matrices whose inverses are F0-matrices are shown to have nonpositive almost principal minors