Potentially nilpotent sign pattern matrices

Generating potentially nilpotent full sign patterns

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 potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentially...

Nilpotent matrices and spectrally arbitrary sign patterns

It is shown that all potentially nilpotent full sign patterns are spectrally arbitrary. A related result for sign patterns all of whose zeros lie on the main diagonal is also given.

Potentially nilpotent tridiagonal sign patterns of order 4

Sign Pattern Matrices that Admit P0 Matrices

A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices. Keywords—Sign pattern matrices, P0 matrices, graph, digraph

Spectrally arbitrary complex sign pattern matrices

An n × n complex sign pattern matrix S is said to be spectrally arbitrary if for every monic nth degree polynomial f(λ) with coefficients from C, there is a complex matrix in the complex sign pattern class of S such that its characteristic polynomial is f(λ). If S is a spectrally arbitrary complex sign pattern matrix, and no proper subpattern of S is spectrally arbitrary, then S is a minimal sp...