===== Linear operator algebra =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$...left $\mathcal R$-module |

| @#FFBB00: definiendum | @#FFBB00: $\langle \mathrm{Hom}(X,X),+,\cdot,*,\rangle \in L(X,X)$ |

| @#55CCEE: context     | @#55CCEE: $\langle \mathrm{Hom}(X,X),+,\cdot\rangle \in \mathcal L(X,X)$ |
| @#55CCEE: context     | @#55CCEE: $*:\mathrm{Hom}(X,X)\times \mathrm{Hom}(X,X)\to \mathrm{Hom}(X,X)$ |

| $ v\in M $ |
| $A,B \in \mathrm{Hom}(X,Y)$ |

| @#55EE55: postulate   | @#55EE55: $(A*B)v = A(B v) $ |

==== Discussion ====
Theorem: A linear operator $A:X\to X$ is bijective if it has an inverse in $L(X,X)$.
==== Parents ====
=== Subset of ===
[[Unital associative algebra]]
=== Refinement of ===
[[Linear operator space]]