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    Can anyone tell me what an eigenframe is? Google doesn't return much. I know of eigenvectors, eigenvalues and eigenspaces but not eigenframes.
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    If anyone knows, this sounds like something pretty cool.
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    (Original post by djpailo)
    Can anyone tell me what an eigenframe is? Google doesn't return much. I know of eigenvectors, eigenvalues and eigenspaces but not eigenframes.
    Would probably be helpful if you gave us the context in which you've seen it being used in.
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    (Original post by djpailo)
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    I believe that you are referring to an Einsteinian concept related to tensors and covariance matrices. Maybe searching for those will lead you closer.
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    (Original post by djpailo)
    Can anyone tell me what an eigenframe is? Google doesn't return much. I know of eigenvectors, eigenvalues and eigenspaces but not eigenframes.
    This is not terminology that I've come across before, but it appears to be used as follows. Any symmetric matrix has a basis in which it is diagonal - and this basis can be formed from the eigenvectors of the matrix - such a basis is called an eigenframe for the matrix and hence for the tensor corresponding to it. Another name used in the literature is a "principal axes frame".
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    (Original post by Gregorius)
    This is not terminology that I've come across before, but it appears to be used as follows. Any symmetric matrix has a basis in which it is diagonal - and this basis can be formed from the eigenvectors of the matrix - such a basis is called an eigenframe for the matrix and hence for the tensor corresponding to it. Another name used in the literature is a "principal axes frame".
    So does this mean your representing the matrix using a different basis, and under this basis, you've made the matrix diagonal and now we have different eigvenvalues for the matrix?

    Thanks for mentioning principal axes frame. I wonder if this refers to principle axes of strain (or stress?) etc that I faintly recollect from structures?
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    (Original post by djpailo)
    So does this mean your representing the matrix using a different basis, and under this basis, you've made the matrix diagonal and now we have different eigvenvalues for the matrix?
    Yes, the matrix is represented in a new basis and it is diagonal in this basis. However, the eigenvalues remain the same - these are invariants of the tensor represented by the matrix. Moreover, if the tensor/matrix varies smoothly from point to point, you'll be able to choose a smooth change of basis that diagonalizes the tensor/metrix at every point. (There'll be some conditions, but I've forgotten them!).

    Thanks for mentioning principal axes frame. I wonder if this refers to principle axes of strain (or stress?) etc that I faintly recollect from structures?
    That's going well beyond my area, but it sounds plausible.
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    (Original post by Gregorius)
    Yes, the matrix is represented in a new basis and it is diagonal in this basis. However, the eigenvalues remain the same - these are invariants of the tensor represented by the matrix. Moreover, if the tensor/matrix varies smoothly from point to point, you'll be able to choose a smooth change of basis that diagonalizes the tensor/metrix at every point. (There'll be some conditions, but I've forgotten them!).



    That's going well beyond my area, but it sounds plausible.
    Okay thanks.
 
 
 
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