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, $(A^*)^* = A\,$ .

Main Page : Linear Algebra

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