x is an evector of A with λ evalue. Show x is an evector of exp(A) with exp(λ) as corresponding evalue.
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Originally Posted by CarmineCortez x is an evector of A with λ evalue. Show x is an evector of exp(A) with exp(λ) as corresponding evalue. I'd start by noting that $\displaystyle e^A = I + A + \frac{A^2}{2!} + .... $ and so $\displaystyle e^Ax = Ix + Ax + \frac{A^2}{2!}x + .... = ....$
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