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Show that a vector space has an eigenvalue if and only if there exists $\dim V-1$ invariant subspace

Since $T$ and its transpose $T^{*}$ have the same characteristic polynomial, $T$ has an eigenvalue if and only if $T^{*}$ has one. If $T^{*}$ has an eigenvalue $w_1$, then extend to a basis $(w_1, w_2,...
Massimiliano Foschi's user avatar
2 votes

Intertwiner space isomorphism with invariante space

I will use the notation $V^G$ for the invariants of a $G$-rep $V$. Tensor-Hom Relation. There is an isomorphism $V^\ast\otimes W\to\hom(V,W)$ where any pure element $\varphi\otimes w$ corresponds to ...
coiso's user avatar
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