(Matlab) How to find inverse using eig

[asynja]

(Matlab) How to find inverse using "eig"

I'm doing a project for Numerical Methods and one of the questions is how to find an inverse of a (random) matrix using Matlab function 'eig'. I know the solution is probably simple, but I almost never used Matlab before, besides, lectures were horrible and notes aren't helping. Anyway, this question bothers me because I can't recall any analytical way of calculating inverse matrix using eigenvalues. There is a consequence of Cayley-Hamilton theorem, where you can find the inverse of A from its characteristic polynomial. But if this is what they're asking to do, then why use 'eig' in Matlab, when there's 'poly' ...

 

[Centrus]

There is a very useful, analytical means by which the inverse of a matrix can be calculated, using the eigenvalues and eigenvectors of the matrix in question. It even has a name: finding the matrix inverse via eigendecomposition. I imagine it would be in your notes, otherwise it is easily found on the web (e.g. http://en.wikipedia.org/wiki/Eigendecomposition#Matrix_inverse_via_eigendecomposition")

I hope that helps!