I remember sitting there staring at the “linear operators”, trying to figure out what the hell they physically did to the eigenvectors - trying to visualize the actual events that were going on in the physical evolution—before it dawned on me that it was just a math trick to extract the average of the eigenvalues.
If anyone else had written this sentence, I would think to myself “Jeez, this guy doesn’t know what he’s talking about.” Did this whole thing start because you don’t understand linear algebra? Linear algebra 1. is an excellent formalism for quantum mechanics and 2. can be taught to high school students, provided they can visualize what matrices do to eigenvectors, i.e. scale them. In any case if you don’t know much linear algebra, this anonymous blog commenter recommends it very much. It’s really useful in all kinds of situations, even for the day to day.