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Jan 9, 2018 at 16:27 vote accept Johnny T.
Jan 9, 2018 at 13:40 comment added Peter Mueller @JohnnyT.: I believe that the article The Principal Axis Theorem Over Arbitrary Fields jstor.org/stable/pdf/2324781.pdf covers what you are interested in.
Jan 9, 2018 at 12:58 comment added Johnny T. Would you happen to know over which field things may work by any chance?
Jan 9, 2018 at 12:04 history edited Peter Mueller CC BY-SA 3.0
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Jan 9, 2018 at 11:58 history edited Peter Mueller CC BY-SA 3.0
added 97 characters in body
Jan 9, 2018 at 11:52 comment added abx Bad example, you want e.g. $\begin{pmatrix} x_1^2 & x_1\\x_1& 0 \end{pmatrix}$.
Jan 9, 2018 at 11:43 history answered Peter Mueller CC BY-SA 3.0