Define a matrix function f(T) of an nxn matrix T by its Taylor series f(T)=f0 +f1T +f2T2+...
Show that if matrix T has the eigenvalues t1,t2...tn, then f(T) has eigenvalues f(t1), f(t2)...f(tn)
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.