If $L$ is an Hermitian matrix associated with an apparatus acting on state $\Psi$, how does the state vector $\Psi$ collapse or change according to matrix arithmetic?
The expectation value for an operator $\hat L$ acting on a wave $\Psi$ is:
$ \langle \Psi \vert \hat L \vert \Psi \rangle =\\ \int_\Omega [\Psi(\mathbf r)]^\dagger \hat L \Psi(\mathbf r) dV $
(Is that what you asked?) (Seems like a density matrix is also used for computing the expected value in more complicated quantum mechanics)
Actually while studying, I had an issue as to when should $\Psi$ collapse and when should it just modify. I now have my answers . Its basically that we say $\Psi$ collapse only if we exclude apparatus outside the quantum system, otherwise when includes, the combined system is in a bell state which upon inspection of apparatus gives the the final state- what we think of a the state $\Psi$ has collapsed to. So in a nutshell there is no dis ambiguity on whether to collapse or just modify.
P.S question was asked by me and now i guess I have an answer.