# On nilpotent interval matrices

Document Type: Research Paper

Authors

1 Faculty of Mathematical Sciences, University of Qom, Qom, Iran

2 School of Mathematics, Iran University of Science & Technology, Tehran , Iran

10.22124/jmm.2019.12669.1239

Abstract

In this paper, we give a necessary and sufficient condition for the powers of an interval matrix to be nilpotent. We show an interval matrix $\it{\bf{A}}$ is nilpotent if and only if $\rho(\mathscr{B})=0$, where $\mathop{\mathscr{B}}$ is a point matrix, introduced by Mayer (Linear Algebra Appl. 58 (1984) 201-216), constructed by the $(*)$ property. We observed that the spectral radius, determinant, and trace of a nilpotent interval matrix equal zero but in general its converse is not true. Some properties of nonnegative nilpotent interval matrices are derived. We also show that an irreducible interval matrix $\bf{A}$ is nilpotent if and only if $| \bf{A} |$ is nilpotent.

Keywords