The Little Book of Linear Algebra

It's crazy that Linear Algebra is one of the deepest and most interesting areas of mathematics, with applications in almost every field of mathematics itself plus having practical applications in almost every quantitative field that uses math.

But it is SOOO boring to learn the basic mechanics. There's almost no way to sugar coat it either; you have to learn the basics of vectors and scalars and dot products and matrices and Gaussian elimination, all the while bored out of your skull, until you have the tools to really start to approach the interesting areas.

Even the "why does matrix multiplication look that way" is incredibly deep but practically impossible to motivate from other considerations. You just start with "well that's the way it is" and grind away until one day when you're looking at a chain of linear transformations you realize that everything clicks.

This "little book" seems to take a fairly standard approach, defining all the boring stuff and leading to Gaussian elimination. The other approach I've seen is to try to lead into it by talking about multi-linear functions and then deriving the notion of bases and matrices at the end. Or trying to start from an application like rotation or Markov chains.

It's funny because it's just a pedagogical nightmare to get students to care about any of this until one day two years later it all just makes sense.

I didn't think any part of linear algebra was boring. I was hooked from the moment I saw Ax=b => x = b/A. Gaussian elimination is a blast, like an actually-productive Sudoku puzzle, and once you have it down you can blaze through the first 2/3rds of an undergrad linear algebra course. I don't consciously try to gain automaticity with math subjects, but matrix-column multiplication I got pretty quickly and now I just have it.

I learned from Strang, for what it's worth, which is basically LU, spaces, QR, then spectral.

I am really bad at math, for what it's worth; this is just the one advanced math subject that intuitively clicked for me.

> I didn't think any part of linear algebra was boring.

My formal linear algebra course was boring as hell, to me. The ~4 lectures my security prof dedicated to explaining just enough to do some RSA was absolutely incredible. I would pay lots of money for a hands-on what-linalg-is-useful-for course with practical examples like that.