Linear Algebra like you've never seen before

Of course, in Mathematics there are rockstar performers too. Take this lecture by Gilbert Strang. The audience is involved, the delivery is brilliantly timed, you see things you never saw before and you leave wanting more. Luckily, there is a whole series of these lectures.

And there are even more of his lectures on the MIT OCW website.

Oh, and since the topic was positive definite matrices, there are 3 ways to tell if you have one (t=47:17 on the video):
1. all the pivots are > 0
2. all the eigenvalues are > 0

3. \quad x^TKx > 0 \quad \forall x \neq 0