Given an $n \times n$ matrix M, I want to optimize the condition number $\text{cond}(AM)$, where $A$ is a $m\times n$ ($m>n$) matrix.
I should write the computation of condition number $\text{cond}(AM)$ in functional form like $f(A)$, so that I can perform operations (such as differentiation) on the matrix $A$. My question is that how should I write this $f(A)$ ?
I'm not sure whether it is a stupid question or not, thank you in advance anyway.