# Inverse Operator

## Main Question or Discussion Point

hello,

given is the Operator L=$$\widehat{1}$$+|u><v|, where $$\widehat{1}$$ means the unity-tensor.

Whats the inverse of L?

I calculated the inverse of L in R^2 but I dont get it back to the bra-ket-notation. Can somebody help?

BTW: Sorry for my bad english!

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The inverse of this operator, assuming <u|v>=0, that is orthogonality, is given by 1-|u><v|.

$$L^{-1}=a\widehat{1}+b|u><v|$$

and using $$LL^{-1}=L^{-1}L=\widehat{1}$$ fix coeficients a and b. This is a general strategy for this kind of algebraic manipulations.

Jon

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