MIT 18.06: Linear Algebra

18.06 is MIT's linear algebra course, made world-famous by Gilbert Strang, whose OCW lectures are arguably the most beloved math course recordings ever published. It covers systems of equations, vector spaces, orthogonality, determinants, eigenvalues, and the SVD with Strang's signature intuition-first style.

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What makes it hard

The four fundamental subspaces and the shift from computing to reasoning about spaces is where students stall — row reduction is easy, but understanding what column space and null space mean takes genuine work. Eigenvalues and the SVD then build directly on that conceptual foundation.

What you'll cover

• Systems of equations and elimination
• Vector spaces and the four fundamental subspaces
• Orthogonality and projections
• Determinants
• Eigenvalues and eigenvectors
• Singular value decomposition

The 18.06 study guide

How to study for MIT 18.06, step by step.

1
Follow each Strang lecture with immediate problems
The OCW lectures are famously watchable, which is exactly the danger — understanding Strang is not the same as doing linear algebra. After every lecture, work the corresponding problems from his textbook the same day.
2
Narrate the four subspaces for every matrix you touch
Column space, null space, row space, left null space — say what each one is for the matrix in front of you. 18.06's real content is this conceptual layer, and it only solidifies through repetition.
3
Connect every computation to the picture
When you row-reduce, ask what happened to the column space. When you project, draw it. Students who keep procedures and concepts linked sail through the eigenvalue and SVD units that build on them.
4
Use the OCW exams to test understanding, not memory
18.06 exams with solutions are posted on OCW. Take them after each unit, attempt fully before checking, and treat conceptual misses as more urgent than computational ones.
5
Run your 18.06 plan through Fennie
Upload the course outline — most self-learners take 18.06 for machine learning foundations — and Fennie's Daily Plan paces lectures, problems, and review to your target date, with subspace-concept quizzes generated from the actual materials. Free to start.
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How Fennie helps with 18.06

Daily Plans pace 18.06 — a course most OCW self-learners take on for machine learning foundations — with concept review before each computational unit, matching Strang's intuition-first approach. Chat through what the null space of a matrix is actually telling you, and quiz yourself linking computations to the subspace picture.

FAQ

Is 18.06 a good way to learn linear algebra?

It's the most-recommended linear algebra course on the internet — Strang's OCW lectures plus his textbook are a complete, free package, and the intuition-first style suits self-study unusually well.

Is 18.06 hard?

The computations are gentle; the conceptual layer — subspaces, rank, orthogonality — is where the effort goes. Students who only learn procedures miss the course's actual content.

Do I need 18.06 for machine learning?

Linear algebra at the 18.06 level is the standard math foundation for ML — eigenvalues, projections, and the SVD show up everywhere from PCA to deep learning.

Pass 18.06 with a plan, not a cram

Upload your 18.06 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.

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