Fun fact: 0 satisfies this matrix equation.
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Isn't that just Vieta's formulas for the polynomial P(x) = det(x I - A)?
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that + Cayley-Hamilton Theorem
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I suspect this only holds for square matrices. (But I suppose any matrix could be padded with zeros to produce a square matrix.)
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as stated in the tweet this only holds for 3x3 matrices, which are indeed square
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I wish someone could explain the intuition behind why the identity is true through a simple description
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Do you know linear algebra?
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If you want more fun stuff on 3x3 matrices (and tensors), there are some neat papers by R.S. Rivlin on Theory of Generators and Invariants
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