First proof in about 20 years

Another hour at lunch today. My brief messing with vectors in Python yesterday was enough to convince me I should brush up on linear spaces. You'd think I'd know those pretty well since what we do here at work really boils down to vector arithmetic on very large dimensional spaces. However, optimizing the mechanics of several trillion calculations is a rather independent skill from deriving the theory.

I brought in an old text and read that for a bit and also went through the exercise of proving the Basis Theorem (mainly because it was the first substantive theorem I came across). I didn't see a real elegant way to prove it, so I just brute forced it by decomposing all the basis elements of the larger set into their sums from the smaller set and showed that there had to be enough non-zero coefficients to force dependence. I was thinking I might be missing something slick, so it was with some relief that I found the author's proof to be quite similar.