# Trying to interpret matrix representations of operators

Say I have a 3x3 operator Q and I find its eigenvectors and eigenvalues. Now i know that those eigenvectors are the same as eigenfunctions so if i act on them with Q i will get the corresponding eigenvalue.

What the question im trying to solve asks is, Measure the quantity Q in state where b is given as a 3x1 matrix. I know how to do it mathematically, I just express as a linear combination of my eigenvectors. But I'm trying to interpret what this means. Is the state some state my wavefunction is in and when I measure it, it will be in a state of one of the eigenvectors of Q?

I am comparing this to Schrodingers cat where before I measure it is in a linear combination of alive and dead and there is a probability that can be alive or dead and when I measure (ie look) the wavefunction collapses to either alive or dead. Am i correct in thinking this way about Q and ?