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How can we show that eigenvalues for $A^*A$ are real and positive without using the Singular Value Decomposition theorem (where $A$ is a complex square matrix and $A^*$ its Hermitian conjugate)?

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    Do you know how to show that the eigenvalues of a self-adjoint matrix are real?2011-05-02
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    Hi, have you tried to prove it by proving $A^* A$ is positive-semidefinite? a hint would be $(A^* Ax, y) = (Ax, Ay)$, where $(\cdot, \cdot)$ is the standard inner product2011-05-02

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