I don’t want to waste time to do formula editting so post image instead ;p
Description
Solution
Comments
The proof consists of 3 important parts:
- A normal matrix, with property
, is diagonalizable by unitary matrix , with , as ; - The column vectors of unitary matrix form a set of orthonormal basis of
. As a result arbitrary vector can be reformulated as ; - The property to be proven is easily shown when the normal matrix is also a diagonal matrix (As is shown in the Lemma).