I'm dealing with problem with matrices that involving cancel out the term of $A B^T - B A^T$, where $A,B\in \mathbb{R}^{d\times n}$.
As far as I know, it is equal to say that $AB^T$ is symmetric, or $\sum_i a_ib_i^T=\sum b_ia_i^T$. However, I'm confused by the meaning of such a canceling, which has kept me away from solving following problem.
Therefore, I want to construct such $A$ and $B$ directly. Could anyone help me out? Thanks a lot in advance!