if K=|a><b| where |a> and |b> are two vectors of the state space.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to show that K can always be written in the form K=gPQ where g is a constant and P and Q are projectors.

this is what I get:

K=|a><b|

<a|b>K=<a|b>|a><b| multiplying by the number <a|b>

<a|b>K=|a><a|b>|<b| inserting that number in between

P=|a><a|

Q=|b><b|

g=<a|b>^-1

so I proved if the vectors are not orthogonal, how to prove it when they are????

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# If K=|a><b| where |a> and |b>

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