I'm reading Quantum Computation and Quantum Information by Nielsen and Chuang (http://mmrc.amss.cas.cn/tlb/201702/W020170224608149940643.pdf). Equation 2.92 on page 85 is a bit confusing to me
if the state of the quantum system is $|\psi\rangle$ immediately before the measurement, then the probability that result $m$ occurs is given by $$p(m) = \langle\psi| M^†_m M_m |\psi\rangle$$
On page 62, they define $\langle\phi | A | \psi\rangle$ as the inner product between $|\phi\rangle$ an $A|\psi\rangle$
So, in this case, A = $M^†_m M_m$, which means the operator $M_m$ is pre-multiplied by it's Hermitian adjoint (the conjugate of the transpose) Then it is matrix-multiplied by the vector $|\psi\rangle$. Then the result of that is inner-producted with $|\psi\rangle$
is that correct?