On nilpotent interval matrices

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})=۰ , where \mathop{\mathscr{B}} is a point matrix, introduced by Mayer (Linear Algebra Appl. ۵۸ (۱۹۸۴) ۲۰۱-۲۱۶), 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.

کلیدواژه ها:

Interval matrix ، nilpotent matrix ، spectral radius