Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Embarassing question about eigenvectors

  1. Oct 15, 2004 #1
    Ok, so let us suppose we have a spinor which is a spin 1/2 state vector


    Now spinors exist in 2 dimensional complex space. How do I find the eigenvalues which correspond to the above eigenvector

    I am confused because we are dealing with eigenvalues for a matrix which is not a square matrix. I know for a square matrix we just find the eigenvalues such that the determinant of the matrix becomes zero. I am not sure how to deal with determinants of non-square matrices however. Helo anybody?
  2. jcsd
  3. Oct 16, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    Eigenvectors only make sense for square matrices. Think about it. Suppose you have a mxn matrix and a nx1 vector. Multiplication will give a mx1 vector. In any case not a scalar multiple of itself.

    The eigenvalues are determined by the matrix. not by the eigenvector itself. Si I can't answer the question:'How do I find the eigenvalues which correspond to the above eigenvector ' if I don't know the matrix.

    EDIT: Whoops. This is physics ofcourse. The matrices you need are probably the Pauli spin-matrices. Use those.
    Last edited: Oct 16, 2004
  4. Oct 16, 2004 #3

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    See the other post on this subject........
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook