induced norm

Suppose $D\in\mathbb{C}^{nxn}$ is a diagonal and positif definite matrix.
Show that the induced matrix norm from the vector norm $\Vert x\Vert_{D}$ is $\Vert A\Vert_{D}=\max\sigma(D^{1/2}AD^{-1/2})$ , that is the maximum singular value of $D^{1/2}AD^{-1/2}$ .
(Note : $D^{1/2}$ denote non negatif definite matrix $X$ satisfy $X^{2}=D$ )

thx for the answer.