Let V be a finite dimensional vector space. Suppose that TE L(V) has dimV distinct eigenvalues...

  

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Let V be a finite dimensional vector space. Suppose that TE L(V) has dimV distinct eigenvalues and that S E L(V) has the same eigenvectors as T (not necessarily the same eigenvalues). Prove that ST = TS. Let V be a finite dimensional vector space. Suppose that TE L(V) has dimV distinct eigenvalues and that S E L(V) has the same eigenvectors as T (not necessarily the same eigenvalues). Prove that ST = TS.

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proof Let dimV n and let 24 222n be the distinct eigenvalues of T Let V V V be ... View the full answer