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matrix_product [2013/09/17 23:01] nikolaj |
matrix_product [2014/03/21 11:11] (current) |
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| ===== Matrix product ===== | ===== Matrix product ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $R$ ... ring | | + | | @#55CCEE: context | @#55CCEE: $R$ ... ring | |
| - | | @#88DDEE: $m,n,k\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $m,n,k\in \mathbb N$ | |
| - | | @#FFBB00: $ *: \mathrm{Matrix}(m,n,R)\times \mathrm{Matrix}(n,k,R)\to \mathrm{Matrix}(m,k,R) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ *: \mathrm{Matrix}(m,n,R)\times \mathrm{Matrix}(n,k,R)\to \mathrm{Matrix}(m,k,R) $ | |
| - | | @#FFBB00: $ (A*B)_{ij}:=\sum_{l=1}^m\ A_{il}\cdot B_{lj} $ | | + | |
| + | | @#55EE55: postulate | @#55EE55: $ (A*B)_{ij}=\sum_{l=1}^m A_{il}\cdot B_{lj} $ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
