Here is my question:
-How do we prove that $\left \| A \right \|=\left \| D \right \|$ where $A$ is a square complex $n$ by $n$ matrix that satisfies: $A=J^{-1}DJ$ where $J$ is unitary (i.e $A$ and $D$ are similar)?
-Can Anyone show me how to prove the above statement?
I started like this: $\left \| A \right \|^{2}=\left ( J^{*}DJ,J^{*}DJ \right )=\left ( DJ,DJ \right )$
and I need to prove that: $\left ( DJ,DJ \right )=...=\left ( D,D \right )=\left \| D \right \|^{2}$?