How to find the eigenvectors of 3 by 3 matrix

[chengcj]

I am currently writing a program to find the 3 eigenvectors of a 3 by 3 matrix. I am only dealing with matrix with real elements and real eigenvalues. I know how to find the eigenvalues. However, I don't know how to find the eigenvectors.

Of course I know that

(Original Matrix) (Eigenvector) = (Eigenvalue) (Eigenvector)

But I don't how to solve this equation to find the eigenvectors.

Is there any method or routine or equations I can use to find the eigenvectors?

[krtxmrtz]

Got to 'Numerical Recipes' and scroll down to chapter 11. There you have a few pdf files explaining the various methods and giving computer recipes in Fortran.

This is part of the "Numerical recipes" book which is entirely available for download. I bought the printed version a few years ago and I think it's quite worth reading it, specially for programmers.