Unformatted text preview: they’re not the exact same subspace. Use this to show that A is diagonalizable iﬀ A T is too. 5. Let A be a square invertible matrix. (a) Show that if A has an eigenvalue λ , then A1 has λ1 as an eigenvalue, and that the eigenvectors of A corresponding to λ are precisely the eigenectors of A1 corresponding to λ1 . (b) Show that A is diagonalizable iﬀ A1 is too. 6. Suppose V is a real vector space and T ∈ L ( V,V ) has no (real) eigenvalues. Prove that every Tinvariant subspace of V has even dimension....
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 Fall '08
 GUREVITCH
 Math, Linear Algebra, real vector space, square invertible matrix

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