Prove in three steps that A T is always similar to A (we know that the s are the same

Chapter 5, Problem 5.6.39

(choose chapter or problem)

Prove in three steps that A T is always similar to A (we know that the s are the same, the eigenvectors are the problem): (a) For A = one block, find Mi = permutation so that M1 i JiMi = J T i . (b) For A = any J, build M0 from blocks so that M1 0 JM0 = J T . (c) For any A = MJM1 : Show that A T is similar to J T and so to J and to A.

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