# General how to find the eigenvectors/values

1. Nov 14, 2005

### johnnyboy2005

this is not an assignment question...but i am just wondering in general how to find the eigenvectors/values for a 3X3 matrix...can someone show me the step by steps with an example?? don't worry, soon i will give back to this web site.

2. Nov 14, 2005

### matt grime

Find the roots of the characteristic equation, solve the linear algbebra problem.

3. Nov 15, 2005

### HallsofIvy

Staff Emeritus
Pretty much the way you find eigenvalues for 2 by 2 matrices- except that it is harder! The characteristic equation is a cubic polynomial equation. Solve that for the eigenvalues.

4. Nov 15, 2005

### mathwonk

an eigenvalue for T is a number c such that Tv = cv for some non zero vector v.

that means (T-c)v = 0, i.e. that T-c is singular, hence has determinant zero.

so look for those c such that det(T-c) = 0. this is a cubic equation in the coefficients of T.

I.e. if you choose a basis for the space, T becomes a matrix and you can calculate this equation and hopefully find its roots.

Or you may know that T is length preserving, say it camer from geometry as a reflection or a rotation, or something like that, and then that imposes restrictions on the possible eigenvalues.

5. Nov 15, 2005

### johnnyboy2005

ah, fantastico