(A paradox for instructors) If AAT = AT A then A and AT share the same eigenvectors

Chapter 6, Problem 22

(choose chapter or problem)

(A paradox for instructors) If AAT = AT A then A and AT share the same eigenvectors (true). A and AT always share the same eigenvalues. Find the flaw in this conclusion: They must have the same S and A. Therefore A equals AT.

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