Let T be an invertible linear operator on a finite-dimensional vector space V. (a)
Chapter 5, Problem 12(choose chapter or problem)
Let T be an invertible linear operator on a finite-dimensional vector space V. (a) Recall that for any eigenvalue A of T, A- 1 is an eigenvalue of T_ 1 (Exercise 8 of Section 5.1). Prove that the eigenspace of T corresponding to A is the same as the eigenspace of T _ 1 corresponding to A"1 . (b) Prove that if T is diagonalizable, then T_ 1 is diagonalizable
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