Learn linear algebra in four months
Four months of consistent work — 45 minutes a day — gets a learner with high-school algebra to real comfort with vectors, matrices, eigenvectors, and the geometry behind them. About 100 hours total. Enough to read machine-learning papers and write the code without faking it.
4 months · ~100 hours · solve systems, decompose matrices, read ML papers
1.3Blue1Brown — Essence of Linear Algebra
Fifteen videos, around four hours. Watch them all before opening anything else. Grant Sanderson teaches what a matrix actually is — a transformation of space — and once you see it, every operation that follows has geometric meaning. Almost no university course teaches it this way and almost every self-taught learner who skipped these videos regrets it.
Free
Essence of Linear Algebra →2.MIT 18.06 — Gilbert Strang
Strang's MIT course is the canonical self-taught linear algebra path. Watch the lectures in order, do the problem sets, take the exams. Strang teaches as if explaining to a friend — column space first, abstraction last. The OCW page has video, notes, problem sets and solutions. Treat it like a real class: three lectures a week, problem set on Sunday.
Free
MIT OCW 18.06 →3.Strang — Introduction to Linear Algebra
The textbook that goes with the course. Read each chapter the day before its lecture. Strang's prose is unusual for a math book — direct, opinionated, almost conversational — and the exercises map cleanly to the OCW problem sets. The sixth edition is current; older editions cost $20 used and lose nothing essential.
~$95 new, ~$20 used (older editions)
Strang's textbook page →If this doesn't fit you
If your goal is purely applied — implementing PCA, understanding gradient descent — and you don't care about proofs, replace Strang with the fast.ai Computational Linear Algebra course. It teaches the same operations through code and skips the formal grounding. You'll be able to use linear algebra. You won't be able to extend it.
Why this path
Linear algebra is the subject most often taught backwards — definitions and determinants before any picture of what's happening. 3Blue1Brown fixes that in a week. Strang's course then builds the algebra on top of a geometric foundation that already makes sense. The book is non-negotiable; watching lectures without doing problems leaves you able to nod along and unable to compute. Skipping problem sets is how this path fails quietly.