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Let A be a (n × n) matrix. Show that A and AT have the same...

Let A be a (n × n) matrix. Show that A and AT have the same characteristic polynomials (and therefore the same eigenvalues). Hint: For any (n×n) matrix B, we have det(BT) = det(B). Remark: Note that, however, it is generally not the case that A and AT have the same eigenvectors!

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