Eigenvalues Definition and 853 Threads

I'm currently taking linear algebra and it has to be the worst math class EVER. It is extremely easy, but I find the lack of application discouraging. I really want to understand how the concepts arose and not simple memorize an algorithm to solve mindless operations, which are tedious. My...

I'm trying to show the relation between L^2 and Lz where L is total angular momentum and Lz is the z component. Given f is an eigenfunction of both L^2 and Lz L^2f = [lamb] f Lz f = [mu] f and L^2 = Lx^2 + Ly^2 + Lz^2 then <L^2> = < Lx^2 + Ly^2 + Lz^2> = <Lx^2> + <Ly^2> + <Lz^2>...

the signature of a metric is often defined to be the number of positive eigenvalues minus negative eigenvalues of the metric. this definition has always seemed a little suspicious to me. eigenvalues are defined for endomorphisms of a linear space, whereas the metric is a bilinear functional...