Now, if it is not clear enough, I'm really new to Mathematica and would immensely appreciate any tips such as where it would be sufficient for me to include the Assumptions and to Simplify at all in a case like this (I would say that the very last FullSimplify, with the Assumptions, would be enough, but am not sure).
Where the last line does not return True, but rather a matrix, in the LHS, with elements different from unit in the diagonal (but, correctly, with $0$ in the off-diagonal). Vecs = Simplify Reals & y \ Reals] įullSimplify = IdentityMatrix, Assumptions -> a > 0 & b > 0 & c > 0 & x \ Reals & y \ Reals] Here is the last thing I have tried: m = Simplify, Assumptions -> a > 0 & b > 0 & c > 0 & x \ Reals & y \ Reals] So, I have to diagonalize a symmetric symbolic matrix $m$ (to be seen below) and obtain the orthogonal transformation $P$ such that $P^TmP=D$ where $D$ is diagonal. I'm aware that there are some questions similar to this here, but none that could solve my problem.
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