I have to solve the problem $b=(A-A^T)x$ for $A\in\mathbb R^{n\times n}$, where $b$ and $x$ are known.
When we need to solve $Ax=b$, with $A$ not invertible, a known result is $x=A^\dagger b$ where $A^\dagger$ is the Moore-Penrose pseudoinverse. In this case I do not care about minimizing the norm of $A$ of any such thing - I just want some $A$ that satisfies $b=(A-A^T)x$. Apart from solving a feasibility optimization problem, is there a known analytical result for this problem?