# General how to find the eigenvectors/values

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.

matt grime
Homework Helper
Find the roots of the characteristic equation, solve the linear algbebra problem.

HallsofIvy
Homework Helper
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.

mathwonk
Homework Helper
2020 Award
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.

ah, fantastico