- #1

- 84

- 0

## Homework Statement

Let A be a real or complex nxn matrix with Jordan decomposition A = [tex]X \Lambda X^{-1}[/tex] where [tex]\Lambda[/tex] is a diagonal matrix with diagonal elements [tex]\lambda_1,...,[/tex] [tex]\lambda_n[/tex]. Show that for any polynomial p(x):

p(A)=[tex]Xp(\Lambda)X^{-1}[/tex]

[tex]p(\Lambda)[/tex] should really be the matrix with p([tex]\lambda_j[/tex]) on its diagonal for j=1,...,n but I couldn't figure out how to make that matrix in latex.

## The Attempt at a Solution

I'm guessing there should be a way to take p of both sides and somehow extract the X and X inverse, but I can't seem to figure it out. Does anyone see anything? Thank you.

Last edited: