Essence of linear algebra preview

Hey everyone!

So I'm pretty excited about the next sequence of videos that I'm doing.

They'll be about linear algebra, which, as a lot of you know,

is one of those subjects that's required knowledge for just about any technical

discipline, but it's also, I've noticed, generally poorly understood by students

taking it for the first time.

A student might go through a class and learn how to compute lots of things,

like matrix multiplication, or the determinant, or cross products,

which use the determinant, or eigenvalues, but they might come out without really

understanding why matrix multiplication is defined the way that it is,

why the cross product has anything to do with the determinant,

or what an eigenvalue really represents.

Oftentimes, students end up well practiced in the numerical operations of matrices,

but are only vaguely aware of the geometric intuitions underlying it all.

But there's a fundamental difference between understanding linear

algebra on a numeric level and understanding it on a geometric level.