An n × n sign pattern A is spectrally arbitrary if given any self-conjugate spectrum there exists a matrix realization of A with that spectrum. If replacing any nonzero entry (or entries) of A by… (More)

A sign pattern is a matrix with entries in {+,−, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing… (More)

Let P (m,n) denote the maximum permanent of an n-by-n lower Hessenberg (0, 1)-matrix with m entries equal to 1. A “staircased” structure for some matrices achieving this maximum is obtained, and… (More)

Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the… (More)

We characterize matrices A ∈ Cn×n whose zero/nonzero pattern requires that the controllability matrix [b Ab Ab . . . An−1b] ∈ Cn×n is of full rank, where b ∈ Cn×1 has exactly one nonzero entry. When… (More)

Block representations of the Drazin inverse of a bipartite matrix A = 2 4 0 B C 0 3 5 in terms of the Drazin inverse of the smaller order block product BC or CB are presented. Relationships between… (More)

The refined inertia (n+, n−, nz, 2np) of a real matrix is the ordered 4-tuple that subdivides the number n0 of eigenvalues with zero real part in the inertia (n+, n−, n0) into those that are exactly… (More)

Dedicated to Ludwig Elsner on the occasion of his 60th birthday. 2 ABSTRACT Two diierent generalizations of the Perron-Frobenius theory to the matrix pencil Ax = Bx are discussed, and their… (More)