Let L V V be an invertible linear operator and let be an eigenvalue of L with associated eigenvector x (a) Show that 1 is an eigenvalue of L 1 with associated eigenvector x (b) State and prove the analogous statement for matrices

Question: Let L: V - V be an invertible linear operator and let be an eigenvalue of L with associated eigenvector x. (a) Show that

Let L: V -→ V be an invertible linear operator and let λ be an eigenvalue of L with associated eigenvector x.
(a) Show that 1 / λ is an eigenvalue of L-1 with associated eigenvector x?
(b) State and prove the analogous statement for matrices?

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