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  3. 1. let v be real vector space (possibly infinite-d

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

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Advance Math

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

  1. Show that there exist square matrices A, B that have the sameeigenvalues, but aren’t similar. Hint: Use the identity matrix asone of the matrices.

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