A+ CATEGORY SCIENTIFIC UNIT

On the orbit of the centralizer of a matrix

Volume 92 / 2002

Ching-I Hsin Colloquium Mathematicum 92 (2002), 243-255 MSC: 47A15, 15A21. DOI: 10.4064/cm92-2-8

Abstract

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 $\{ A \}'$.

Authors

  • Ching-I HsinDivision of Mathematics
    Minghsin Institute of Technology
    Hsinchu County 304, Taiwan
    e-mail

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