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.