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linear_operator_algebra [2013/09/06 22:04]
127.0.0.1 external edit
linear_operator_algebra [2014/03/21 11:11] (current)
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 ===== 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 ====
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