what does it mean, if you say that $x$ is an eigenvalue of an element $g \in G$, where $G$ is a group? I know this definition just for matrices, not for elements.
Eigenvalue of an element
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linear-algebra
abstract-algebra
representation-theory
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1So, if you're given a representation $\phi:G\to {GL}_n(\mathbb{R})$ or something of this nature, then a natural way to define an eigenvalues of $g\in G$ is to declare them to be the same as the eigenvalues of $\phi(g)$. However, this definition should depend on the representation. I'm pretty sure this is the correct idea, but I'm not super familiar with it can someone confirm? – 2012-08-29
1 Answers
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Given a group representation $\rho: G\to GL(V)$ you have a matrix associated to every element $g\in G$, namely $\rho(g)$.