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arpon
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Homework Statement
If ##AA^T=A^TA##, then prove that ##A## and ##A^T## have the same eigenvectors.
Homework Equations
The Attempt at a Solution
##Ax=\lambda x##
##A^TAx=\lambda A^Tx##
##AA^Tx=\lambda A^Tx##
##A(A^Tx)=\lambda (A^Tx)##
So, ##A^Tx## is also an eigenvector of ##A##.
What should be the next steps?