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Matrix product
Definition
| $R$ … ring |
| $m,n,r\in \mathbb N$ |
| $ *: \mathrm{Matrix}(m,n,R)\times \mathrm{Matrix}(n,r,R)\to \mathrm{Matrix}(m,r,R) $ |
| $ (A*B)_{jk}:=\sum_{l=1}^m\ A_{jl}\cdot B_{lk} $ |
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
