So I have a set of 15 $4\times 4$ matrices which I call $X_i, (i=1,2..15)$ and a set of 6 $4\times 4$ matrices which I call $y_j, (j=1,2...6)$. Now I have to calculate $(X_i y_j)-(y_j X_i^*)$ for different values of $i$ and $j$, where $*$ stands for Complex conjugate. Is there a simple command (with perhaps loops) in mathematica using which I can calculate all the 90 results instead of multiplying these matrices individually 90 times?
Define some matrices.
Or to follow your naming convention of variable names with subscripts:
Define the number of Xs and ys: