We really never got this subject. I'll try to walk through Cayley-Klein. In the process, we'll try to prove all results, e.g., the fact that the Hermitian quality of a matrix survives a unitary similarity transformation; that the trace and determinant survive any sort of similarity transformation, whether unitary or not; etc. We'll also take a survey of whether anyone has any intuition for the "trace" of a matrix, what the hell it means. I can share what I read. We can try to puzzle it out. I also will describe my linear algebra "puzzle" and see if anyone else believes it's worth any thought. Etc. We'll also try to assign a "lecturer" for next time.
Remember Woody Allen's observation that 90% life is just showing up.