I have to prove or disprove this statement. I am not sure how to do it. I think we cannot be certain that it will be positive definite, but how to state the proof?
2026-03-27 10:09:33.1774606173
For any non-singular square matrix A, is A + A' a Positive Definite matrix?
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The statement is not true. For example, consider $$ A = \pmatrix{0&-1\\1&0}. $$