Let A be an n x n real matrix with the property that AT A Show that if Ax x for some nonzero vector x in Cn, then, in fact, A is real and the real part of x is an eigenvector of A

Question: Let A be an n x n real matrix with the property that AT = A. Show that if Ax = x for some nonzero

Let A be an n x n real matrix with the property that AT = A. Show that if Ax = λx for some nonzero vector x in Cn, then, in fact, A is real and the real part of x is an eigenvector of A.

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