I have a bit of problem with zero eigenvectors and zero eigenvalues. On one hand, there seems to be nothing in the definition that forbids them, and they even seem necessary to allow because an eigenvalue can serve as a measurement and zero can be a measurement, and if there is a zero eigenvalue then it will be a term in a diagonalized matrix, so that one has a zero eigenvector as well (a column vector of the diagonal matrix with the zero eigenvalue). So far, so good. But on the other hand, if the zero eigenvector is allowed, then every value in the field would be an eigenvalue, hence making it a bit trivial, no?(adsbygoogle = window.adsbygoogle || []).push({});

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# Zero eigenvalues or eigenvectors

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