Why is the 2-norm of A^k equal to 2-norm of T^k?

[vabamyyr]

Let Q^H * A * Q = T = D + N be Schur decomposition of A. D is a diagonal matrix with eigenvalues of A and N is strictly upper triangular matrix. This sentence is used in a proof which I am not going to state but at some point it states that ||A^k|| 2 norm = ||T^k|| 2 norm for k>=0. I don't understand
where this equality comes from. I tried to work this equality out with an example of taking

 

[matt grime]

You can help yourself, and us, by using the latex formatting in this forum to make it clear what it is you're asking. Note the text in the reply box is not formatted literally.

 

[vabamyyr]

The problem is simple: why is the 2-norm of A^k equal to 2-norm of T^k?