===== Matrix product =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $R$ ... ring | 
| @#55CCEE: context     | @#55CCEE: $m,n,k\in \mathbb N$ | 

| @#FFBB00: definiendum | @#FFBB00: $ *: \mathrm{Matrix}(m,n,R)\times \mathrm{Matrix}(n,k,R)\to \mathrm{Matrix}(m,k,R) $ |

| @#55EE55: postulate   | @#55EE55: $ (A*B)_{ij}=\sum_{l=1}^m A_{il}\cdot B_{lj} $ |

==== Discussion ====
For square matrices, the matrix product is associative. And also for general matrices, we still have $(A*B)*'C=A*''(B*'''C)$, where the four binary functions are the matrix products for the suitable dimensions.
==== Parents ====
=== Subset of ===
[[Matrix]], [[Function]]