Physics, Quantum Physics, Quantum Mechanics, Quantum, Mathematics.
basis vector act from the side: Where in the 3rd step I used the fact that ⟨j|i⟩ is just the inner product between two orthonormal basis vectors which yields the Kronecker delta (1 when i = j and 0 when i ≠ j). Now, here is where things get interesting because if we let j be i in the above