Here is a link which better describes what I am trying to prove:
The Matrix Exponential as a Limit of Powers
if anyone could help me get further I would really appreciate it!
Trying to solve a proof for Linear Algebra:
for a in the set of complex numbers, e^a = lim k-> ∞ (1 + a/k)^k
Establish the matrix analog for any A in the set of real nxn square matrices
e^A = lim k->∞ (I + A/k)^k
I started off by trying the following:
A = P D P^-1
A^k = P D^k P^-1
e^At = P e^D^kt P^-1
not sure where to go from here or if this is the right thought process, I would appreciate any help I can get!