2002Colloquium MathematicumOpen access

On the orbit of the centralizer of a matrix

Ching-I Hsin

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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 invari

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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 invari

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Available 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 invari

Key concepts: Centralizer and normalizer, Mathematics, Orbit (dynamics), Matrix (chemical analysis), Action (physics), Combinatorics, Pure mathematics, Physics

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