I have a matrix $A$ of dimension $k \times n$, and also $n$ matrices $B_{i}, i \in [n]$ each of dimension $k \times k$.
I want to define a matrix $C$, $c_{j}$ such that the $j^{th}$ column of $C$ is given as $B_{j} a_{j}$.
I am essentially constructing $C$ by multiplying each column of $A$ by a different matrix.
Is this a standard operation? I was unable to find such a product anywhere. I tried looking at the $B_{i}s$ as a tensor, but still could not find anything.