# Differences

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 matrix_product [2013/09/17 23:01]nikolaj matrix_product [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/17 23:29 nikolaj 2013/09/17 23:01 nikolaj 2013/09/17 23:01 nikolaj 2013/09/17 23:00 nikolaj 2013/09/17 23:00 nikolaj 2013/09/17 22:59 nikolaj 2013/09/17 18:12 nikolaj 2013/09/17 18:10 nikolaj 2013/09/17 18:10 nikolaj old revision restored (2013/09/17 17:39) Next revision Previous revision 2013/09/17 23:29 nikolaj 2013/09/17 23:01 nikolaj 2013/09/17 23:01 nikolaj 2013/09/17 23:00 nikolaj 2013/09/17 23:00 nikolaj 2013/09/17 22:59 nikolaj 2013/09/17 18:12 nikolaj 2013/09/17 18:10 nikolaj 2013/09/17 18:10 nikolaj old revision restored (2013/09/17 17:39) Line 1: Line 1: ===== 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 ====