SOLVED: Let V be a real vector space (possibly infinite-dimensional), S, T ∈ L(V), and S be invertible. Prove that 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 with an eigenvalue λ in terms of the eigenvectors of T associated with 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.
SOLVED: Let V be a real vector space (possibly infinite-dimension…
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