- #1

- 35

- 0

## Homework Statement

Define a matrix function f(T) of an nxn matrix T by its Taylor series f(T)=f

_{0}+f

_{1}T +f

_{2}T

^{2}+...

Show that if matrix T has the eigenvalues t

_{1},t

_{2}...t

_{n}, then f(T) has eigenvalues f(t

_{1}), f(t

_{2})...f(t

_{n})

## Homework Equations

## The Attempt at a Solution

I am at a loss of how to prove this, could someone help me with this problem? I have no idea where to start.