47 MIMO dominoes

Let $A,B,C,D$ be complex matrices with shapes $A$ $(n\times n)$; $B$ $(n\times k)$; $C$ $(m\times n)$; $D$ $(m\times k)$ Recall

so we form $m\times k$ matrices $CB,CAB,D$. The operations in a MIMO system are:

(i) taps;

(ii) summing junctions, which simply add matrices of the same shape;

(iii) differentiation $d/dt$ , which operates on all the entries of the matrix;

(iv) integration $\int$ which operates on all the entries of the matrix;

(v) matrix amplifiers $U\mapsto BU$, which can change the shape of $U$ to $BU$. Usually, we multiply on the left by the matrix.