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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This can’t be true. For example, the Pauli matrices have identical eigenvalues, but different eigenvectors. I wonder how the paper deals with that.
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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Of course, but if I tell you “I’ve got a 2x2 matrix with eigenvalues +1 and -1, give me the eigenvectors”, what would you respond with? (1,0) and (0,1)? (1,1) and (1,-1)?
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well you need the matrix! you can't just give me random numbers lol
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