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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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)?
well you need the matrix! you can't just give me random numbers lol
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Yes, this is the whole point. The eigenvectors are not completely determined by the eigenvalues, they depend on the matrix
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But if I have the matrix and the eigenvalues, then I already know how to find the eigenvectors! I think your excitement is coming from a deeper knowledge of linear algebra than I possess. :D
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