```Date: May 24, 2010 8:37 PM
Author: luca
Subject: Computation of the matrix exponential

Hi,i have the following problem: given a 3x3 real matrix, compute exp(A).I need a really fast way to do this. I have searched a bit withgoogle, but it seems to me thatcomputing the matrix exponential is not so simple, at least if yourmatrix does not have a specialstructure (for example A=diagonal matrix).I have found a simple method that use the diagonalization of A. If Ahas 3 distinct eigenvalues, than computeA=PDP^-1, where P is the matrix of the eigenvectors, D is a diagonalmatrix (whose diagonal elements arethe eigenvalues of A). Than, exp(A) = P exp(D) P^-1. Since P^-1 isfast enough and exp(D) is simpleto compute, this should be a fast method.But, the problem is: i am not sure that the matrix A will always have3 distinct eigenvalues...what happensif this does not happen? Can i use that formula even if 2 (or allthree) eigenvalues are equal?Are there any other ways to compute exp(A) in a fast way?Thank you,Luca
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