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 linear_operator_algebra [2013/09/13 21:39]nikolaj linear_operator_algebra [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/13 21:40 nikolaj 2013/09/13 21:39 nikolaj 2013/09/06 22:04 external edit2013/08/31 18:29 nikolaj 2013/08/31 18:01 nikolaj 2013/08/31 18:01 nikolaj 2013/08/31 17:59 nikolaj 2013/08/31 17:57 nikolaj 2013/08/31 17:55 nikolaj 2013/08/31 17:55 nikolaj created Next revision Previous revision 2013/09/13 21:40 nikolaj 2013/09/13 21:39 nikolaj 2013/09/06 22:04 external edit2013/08/31 18:29 nikolaj 2013/08/31 18:01 nikolaj 2013/08/31 18:01 nikolaj 2013/08/31 17:59 nikolaj 2013/08/31 17:57 nikolaj 2013/08/31 17:55 nikolaj 2013/08/31 17:55 nikolaj created Line 1: Line 1: ===== Linear operator algebra ===== ===== Linear operator algebra ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $X$...left $\mathcal R$-module | + | @#55CCEE: context ​    | @#55CCEE: $X$...left $\mathcal R$-module | - | @#FFBB00: $\langle \mathrm{Hom}(X,​X),​+,​\cdot,​*,​\rangle \in L(X,X)$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\langle \mathrm{Hom}(X,​X),​+,​\cdot,​*,​\rangle \in L(X,X)$ | - | @#88DDEE: $\langle \mathrm{Hom}(X,​X),​+,​\cdot\rangle \in \mathcal L(X,X)$ | + | @#55CCEE: context ​    | @#55CCEE: $\langle \mathrm{Hom}(X,​X),​+,​\cdot\rangle \in \mathcal L(X,X)$ | - | @#88DDEE: $*:​\mathrm{Hom}(X,​X)\times \mathrm{Hom}(X,​X)\to \mathrm{Hom}(X,​X)$ | + | @#55CCEE: context ​    | @#55CCEE: $*:​\mathrm{Hom}(X,​X)\times \mathrm{Hom}(X,​X)\to \mathrm{Hom}(X,​X)$ | | $v\in M$ | | $v\in M$ | | $A,B \in \mathrm{Hom}(X,​Y)$ | | $A,B \in \mathrm{Hom}(X,​Y)$ | - | @#55EE55: $(A*B)v = A(B v)$ | + | @#55EE55: postulate ​  | @#55EE55: $(A*B)v = A(B v)$ | ==== Discussion ==== ==== Discussion ==== Line 19: Line 19: [[Unital associative algebra]] [[Unital associative algebra]] === Refinement of === === Refinement of === - [[Linear operator]] + [[Linear operator ​space]]