trying to be a mile wide AND a mile deep
Which of the following are vector spaces over the scalar field R of real numbers? A) U = (R x R, +U, *U) where (a1, a2) +U (b1, b2) = (a1 + 2b1, a2 + 3b2) and *U is the usual scalar multiplication B) V = (R x R, +V, *V) where (a1, a2) +V […]
I include this because it wasn’t in any of the books in which I looked for it when I last taught linear algebra. Exercise: show that if a vector space (over the real numbers) has at least two vectors, it has infinitely many. Simple proof: If V has two vectors, one of them is nonzero. […]
When I was an undergraduate, we had an entire class dedicated to making the transition from calculus-type mathematics to abstract upperclass-level mathematics. We learned basic logic and set notation and manipulation, proof structures, and induction, proving simple number theory results that didn’t require additional new concepts beyond induction. I got to teach such a course […]
In February of 2011, I gave a talk to the Dartmouth Math Club about linear algebra. This post replicates the page of resources I made for the club members related to that talk, and adds one new one. Slides from the talk. Pdf about uses of linear algebra. From Oliver Knill, Harvard Math, near the […]