Absolutely Amazing Physicists (!) discover a new fundamental and amazing mathematical fact: You can get the Eigenvectors of a matrix using ONLY its Eigenvalues https://arxiv.org/pdf/1908.03795.pdf …pic.twitter.com/Mt797mmqDk
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I felt like i had seen it in strang either the svd or spectral form ..but maybe not . You can write eigen vectors using eigen values in clever ways , this looks eerily similar
no! .. of course you USE eigenvalues to find the eigenvectors, but the fact that they are completely determined by them is crazy
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This can’t be true. For example, the Pauli matrices have identical eigenvalues, but different eigenvectors. I wonder how the paper deals with that.
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No, the eigenvectors of any one of the three pauli matrices span the entire 2x2 vector space.. so the eigenvectors of the other two are just a linear combination of the one we chose to diagonalize (usually σz)
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I will wait for others to opine also . I know tao said what he said . I am not surprised by that form still
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well you should be .. i don't know what to tell you
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The formula in the paper assumes you know the eigenvalues of various submatrices M of the matrix as well, or am I misreading it?
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You’re right! I was addressing comments of a similar concern .. I’ve updated the thread and addressed those. Thanks!
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