As the title says. Is the matrices $A^*A$ and $AA^*$ hermitian (symmetric if $A$ is real)?
Is the matrix $A^*A$ and $AA^*$ hermitian?
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linear-algebra
matrices
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0Thanks! These hints really helped. Remember this from the lectures now. How could I not see this? – 2012-01-16
1 Answers
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Check the definition of hermitian. This is not too hard, you just have to use that $(AB)^*=B^*A^*$. You don't need that $A$ is invertible in this proof, the statement is even true for $A$ not a square.