Embarassing question about eigenvectors

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SUMMARY

The discussion centers on the calculation of eigenvalues for spinors in quantum mechanics, specifically spin 1/2 state vectors. Participants clarify that eigenvalues are defined for square matrices, and the confusion arises when attempting to apply this concept to non-square matrices. The Pauli spin matrices are identified as the appropriate matrices to use for determining eigenvalues related to spinors. The key takeaway is that without a square matrix, one cannot derive eigenvalues from eigenvectors.

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Ed Quanta
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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 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?
 
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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.
 
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