On nilpotent interval matrices

Document Type : Research Article


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

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


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.