Α1, A2, …An are the eigenvectors of A (with algebraic multiplicity) the 1/A1, 1/A2, …,1/A n are the eigenvalues of A^-1 (with algebraic multiplicity) how would i show this? any suggestions?
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I assume you meant "eigenvalues", not "eigenvectors". Hint: Consider the action of on an eigenvector of A.
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