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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 ==== |