Getting into linear algebra
Three ways in, depending on how you learn. They cover the same ground and link into each other. If you only open one, open the field guide.
New to linear algebra? Start here for a quick readiness check, what to read alongside, and which guide to open first.
A field guide to matrices
Fifteen species of $2 \times 2$ matrix, each drawn by what it does to the plane, with field marks for telling look-alikes apart. There's also a key that identifies any matrix you type in.
For: visual thinkers, and anyone who's diagonalised things without knowing what that looks like.
What everyone asks
I went through the 2,000 most upvoted linear algebra questions on Math Stack Exchange and built a guide from them, in the order people get stuck.
For: people who've taken the course and still feel shaky.
how questions get the traffic. why questions get the votes.
Thirty problems
No explanations. Solve the problems in order and you'll have proved rank–nullity, built the determinant from three rules, and reached the spectral theorem yourself. There are hints if you need them.
For: people who learn by doing, or anyone who wants it to stick.
Let $v_1 = (1,2,3)$, $v_2 = (4,5,6)$, $v_3 = (7,8,9)$. Find $a, b, c$, not all zero, with $av_1 + bv_2 + cv_3 = 0$.
Also in this series: group theory.