Geodesic
On the orbit of the centralizer of a matrix
Ching-I Hsin1
1 Division of Mathematics Minghsin Institute of Technology Hsinchu County 304, Taiwan
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 $\{ A \}'$.
DOI : 10.4064/cm92-2-8
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

Ching-I Hsin 1

1 Division of Mathematics Minghsin Institute of Technology Hsinchu County 304, Taiwan 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm92-2-8/

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