Now we move on a little with our understanding of operators.
A ket vector followed by a bra vector is an example of an operator.
For example the operator which projects a vector onto the eigenstate is
The sum of the projection operators is 1, if we sum over a complete set of states, like the eigenstates of a Hermitian operator.
The same is true for definite momentum states.
We can form a projection operator into a subspace.
Jim Branson 2013-04-22