1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

General how to find the eigenvectors/values

  1. Nov 14, 2005 #1
    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.:biggrin:
  2. jcsd
  3. Nov 14, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Find the roots of the characteristic equation, solve the linear algbebra problem.
  4. Nov 15, 2005 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    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.
  5. Nov 15, 2005 #4


    User Avatar
    Science Advisor
    Homework Helper

    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.
  6. Nov 15, 2005 #5
    ah, fantastico
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: General how to find the eigenvectors/values