Differences
This shows you the differences between two versions of the page.
|
matrix_product [2013/09/17 23:29] nikolaj |
matrix_product [2014/03/21 11:11] |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ===== Matrix product ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $R$ ... ring | | ||
| - | | @#88DDEE: $m,n,k\in \mathbb N$ | | ||
| - | |||
| - | | @#FFBB00: $ *: \mathrm{Matrix}(m,n,R)\times \mathrm{Matrix}(n,k,R)\to \mathrm{Matrix}(m,k,R) $ | | ||
| - | |||
| - | | @#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]] | ||
