linear_operator

Linear operator algebra

context

$X$ …left

$\mathcal R$ -module

definiendum

$\langle \mathrm{Hom}(X,X),+,\cdot,*,\rangle \in L(X,X)$

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

$v\in M$

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

postulate

$(A*B)v = A(B v)$

Theorem: A linear operator $A:X\to X$ is bijective if it has an inverse in $L(X,X)$ .