LA7

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Show that AA^{*}\, is self-adjoint.

Let A^{*}\, be the adjoint of the matrix A\,. Then, for the matrix AA^{*}\,

(AA^{*})^{*}\, =(A^{*})^{*}A^{*}\,
=AA^{*}\,

Therefore, AA^{*}\, is the adjoint of AA^{*}\,, or, in other words, AA^{*}\, is self-adjoint.


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