The discussion revolves around the properties of matrix exponentials, specifically relating to eigenvalues and eigenvectors of a matrix A. Participants are tasked with demonstrating a relationship involving the matrix exponential and its action on eigenvectors.
The discussion is ongoing, with some participants offering insights into the nature of the matrix exponential and its convergence properties. There are attempts to guide the original poster towards considering the implications of the eigenvalue equation and the behavior of matrix powers.
One participant notes the lack of effort shown by the original poster, which has led to a lock on the thread. There is a mention of a preference for notation regarding vectors, indicating a potential point of confusion in the discussion.
The power series is quite instructive. Each side is some matrix that is a function of ##A##. What happens if you multliply each side by an eigenvector of A? The idea is there are a lot of moving parts here... if you can find a fixed point maybe it isn't so hard.BearY said:Homework Equations
##e^A=\sum\limits_{n=0}^\infty\frac{1}{n!}A^n##
BearY said:Homework Statement
Show that if ##λ##and ##V ## are a pair of eigenvalue and eigenvector for matrix A, $$e^AV=e^λV$$
Homework Equations
##e^A=\sum\limits_{n=0}^\infty\frac{1}{n!}A^n##
The Attempt at a Solution
I don't know where to start.