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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


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    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

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    See the other post on this subject........
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