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Jan 31, 2021 at 17:26 comment added A.Z. If $q$ is the zero vector then $Xq$ and $q$ are not linear independent. Is $q=0$ allowed for your problem?
Jan 29, 2021 at 16:53 comment added Denny I just come up with such possible function. Not sure if it is correct. $f(X,Q) = XQ-QX$. It is symmetric, rank 2 with $\{Xq, q\}$ if $Xq, \, q$ are L. I. And trace of $f(X,Q)$ is zero since tr$(XQ) = q^TXq$, so tr$(f)=q^TXq-q^TXq=0$.
Jan 29, 2021 at 14:03 review First posts
Jan 29, 2021 at 15:26
Jan 29, 2021 at 13:57 history answered A.Z. CC BY-SA 4.0