Let $A \in \mathbb{C}^{I\times J}$ be the so-called reference matrix, which will be estimated by an algorithm. The estimate will be called $A'\in \mathbb{C}^{I'\times J'}$, and might have other dimensions than $A$. For the case that the dimensions of $A$ have been correctly estimated (i.e $I' = I$ and $J' = J$), the error $e$ shall be computed by $e=\frac{||A'-A||_2}{||A||_2}$.
What would be a nice extension to this way of error-measurement for the case that $A$ and $A'$ do not have the same size?
Thanks in advance for your input! :)