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Jordan types of commuting nilpotent matrices

Semra Ozturk
대한수학회 (The Korean Mathematical Society)|2018.10|대한수학회논문집 (Communications of the KMS)|제33권 제4호|pp. 1097-1102

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참고문헌

키워드

Jordan canonical formJordan typepairwise commuting nilpotent matrices
주제분류수학

초록

Let $A$ and $B$ be matrices which are polynomials in $r$ pairwise commuting nilpotent matrices over a field. We give a sufficient condition for the null space of $A^i$ to equal that of $B^i$ for all $i$, in particular, for $A$ and $B$ to be similar.

Abstract

Let $A$ and $B$ be matrices which are polynomials in $r$ pairwise commuting nilpotent matrices over a field. We give a sufficient condition for the null space of $A^i$ to equal that of $B^i$ for all $i$, in particular, for $A$ and $B$ to be similar.

참고문헌 (5)

  1. J. F. Carlson, "Modules of constant Jordan type", J. Reine Angew. Math, 614, pp.191~234 (2008)
  2. S. O. Kaptanoglu, "Commuting nilpotent operators and maximal rank", Complex Anal. Oper. Theory, 4(4), pp.901~904 (2010)
  3. -module, "New York J. Math", 2011, 307~313
  4. S. O. Kaptanoglu, "p-power points and modules of constant p-power Jordan type", Comm. Algebra, 39(10), pp.3781~3800 (2011)
  5. S. O. Kaptanoglu, "Restricted modules and conjectures for modules of constant Jordan type", Algebr. Represent. Theory, 17(5), pp.1437~1455 (2014)

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