1. Let V be real vector space (possibly infinite-dimensional), S, T ∈ L(V ), and S...

1. Let V be real vector space (possibly infinite-dimensional), S, T ∈ L(V ), and S be in- vertible. Prove λ ∈ C is an eigenvalue of T if and only if λ is an eigenvalue of STS−1. Give a description of the set of eigenvectors of STS−1 associated to an eigenvalue λ in terms of the eigenvectors of T associated to λ.

Show that there exist square matrices A, B that have the same eigenvalues, but aren’t similar. Hint: Use the identity matrix as one of the matrices.

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Expert Solution

Colby Messinger answered 1 year ago

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