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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 (a)
    b

    Now spinors exist in 2 dimensional complex space. How do I find the eigenvalues which correspond to the eigenvector
    (a)
    b


    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

    Dr Transport

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    Gold Member

    in spin 1/2 space, the eigen vectors are usually found using the z component of the angular momentum. Use the Pauli matricies for [tex] S_{z} [/tex] to find the eigenvalues and vectors.
     
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