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Unformatted text preview: theyre not the exact same subspace. Use this to show that A is diagonalizable i A T is too. 5. Let A be a square invertible matrix. (a) Show that if A has an eigenvalue , then A-1 has -1 as an eigenvalue, and that the eigenvectors of A corresponding to are precisely the eigenectors of A-1 corresponding to -1 . (b) Show that A is diagonalizable i A-1 is too. 6. Suppose V is a real vector space and T L ( V,V ) has no (real) eigenvalues. Prove that every T-invariant subspace of V has even dimension....
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- Fall '08