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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

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

    HallsofIvy

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    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

    mathwonk

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    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
     
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