TITLE: Properties of the Product of a Square Matrix with its Conjugate Transpose
QUESTION [1 upvotes]: Let $A$ be a square complex matrix. What special properties are possessed by $AA^H$, where $^H$ denotes the conjugate transpose?
One property I am aware of is that $AA^H$ is Hermitian, i.e. $AA^H=(AA^H)^H$ - in fact, this is true even when $A$ is not square. 
Are there any other special properties of $AA^H$?

REPLY [2 votes]: Yes.  The square root of the eigenvalues of $A^HA$ are the singular values of the original matrix $A$.
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