On the orbit of the centralizer of a matrix
Colloquium Mathematicum, Tome 92 (2002) no. 2, pp. 243-255
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $A$ be a complex $n \times n$ matrix. Let $\{ A \}'$
be its commutant in $M_n({\mathbb C})$, and $C(A)$ be its centralizer in
${\rm GL}(n, {\mathbb C})$. Consider the standard $C(A)$-action on ${\mathbb C}^n$.
We describe the $C(A)$-orbits via invariant subspaces of $\{
A \}'$. For example, we count the number of $C(A)$-orbits as well as that
of invariant subspaces of $\{ A \}'$.
Keywords:
complex times matrix its commutant mathbb its centralizer mathbb consider standard action mathbb describe orbits via invariant subspaces example count number orbits invariant subspaces
Affiliations des auteurs :
Ching-I Hsin 1
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author = {Ching-I Hsin},
title = {On the orbit of the centralizer of a matrix},
journal = {Colloquium Mathematicum},
pages = {243--255},
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volume = {92},
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year = {2002},
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Ching-I Hsin. On the orbit of the centralizer of a matrix. Colloquium Mathematicum, Tome 92 (2002) no. 2, pp. 243-255. doi: 10.4064/cm92-2-8
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