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On nilpotent interval matrices | ||
| Journal of Mathematical Modeling | ||
| مقاله 6، دوره 7، شماره 2، شهریور 2019، صفحه 251-261 اصل مقاله (276.83 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2019.12669.1239 | ||
| نویسندگان | ||
| Effat Golpar raboky* 1؛ Tahereh Eftekhari2 | ||
| 1Faculty of Mathematical Sciences, University of Qom, Qom, Iran | ||
| 2School of Mathematics, Iran University of Science & Technology, Tehran , Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Interval matrix؛ nilpotent matrix؛ spectral radius | ||
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