For $A\in\mathbb F^{m\times n}$, $B\in\mathbb F^{n\times p}$ and $x\in\mathbb F^p$, $(AB)x=A(Bx)$. Both sides have $i$th entry $\sum_j\sum_k a_{ij}b_{jk}x_k$. This explains why matrix multiplication represents composition: first apply $B$, then $A$.
Parents
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.