- Summary
- Product of two projection operators

In Principles of Quantum mechanics by shankar it is written that

Pi is a projection operator and Pi=|i> <i|.

Then PiPj= |i> <i|j> <j|= (δij)Pj.

I don't understand how we got from the second result toh the third one mathematically.I know that the inner product of i and j can be written as δijbut how do we get to Pj in the final result from the second result?

Pi is a projection operator and Pi=|i> <i|.

Then PiPj= |i> <i|j> <j|= (δij)Pj.

I don't understand how we got from the second result toh the third one mathematically.I know that the inner product of i and j can be written as δijbut how do we get to Pj in the final result from the second result?