We have two matrices, $A$ and $B$, representing two different probability distributions, with dimensions, $m*n$ and $k*n$, respectively.
How can we calculate the Bhattacharya distance or another measure of similarity or dissimilarity between $A$ and $B$?
Here, $m$ and $k$ denote the number of variables captured by the two matrices $A$ and $B$. In general, $m$ and $k$ are not equal.
$n$ is the number of observations, which is the same across the two distributions.
Related Broader Question:
Combining Bhattacharya Distance (or A Measure of Similarity) --- across Different Variables (Properties)