Proving that every eigenvalue is $Positive$.

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In completion of this question :

Understanding a step in a solution.

The link contains the proof that $\lambda $ is nonnegative, but the question requires it to be positive, can anyone help me to prove this?

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If $A$ is the zero matrix then $0$ is an eigen value of $A^{H}A$. You cannot prove that the eigen value is $>0$.