LA5

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Show that (A^{*})^{*}=A\,

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

\langle A^{*}x,y\rangle =\overline {\langle y,A^{*}x\rangle }
=\overline {\langle Ay,x\rangle }
=\langle x,Ay\rangle

Therefore, A\, is the adjoint of A^{*}\,, or, in other words, (A^{*})^{*}=A\,.


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