Let V be a complex vector space with ordered basis B = {e1, e2, e3, e4}. Consider the linear transfo ...

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Let V be a complex vector space with ordered basis B = {e1, e2, e3, e4}. Consider the linear transformation T such that T(e1) = e2, T(e2) = e3, T(e3) = e4, T(e4) = e1. (a) Find the matrix representation of T with respect to B. (b) Find the eigenvalues of T. (c) Find the eigenvectors of T. (d) Show that the eigenvectors of T form a basis C of V. (e) Find the transition matrix P_{B,C}.