Spectral Theorem - University of California, Berkeley
https://inst.eecs.berkeley.edu/~ee127/sp21/livebook/l_sym_sed.html
Feb 4, 2021 · Spectral theorem. An important result of linear algebra, called the spectral theorem, or symmetric eigenvalue decomposition (SED) theorem, states that for any symmetric matrix, there are exactly (possibly not distinct) eigenvalues, and they are all real; further, that the associated eigenvectors can be chosen so as to form an orthonormal basis.
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