The journey begins with solving simultaneous equations. You will learn about Gaussian Elimination, row exchanges, and LU Decomposition (
Linear algebra is a "doing" sport. MIT OCW provides the solutions to Professor Strang's problems, which is vital for self-correction.
Professor Strang maintains a personal MIT faculty page dedicated to his textbooks, such as Introduction to Linear Algebra (now in its 6th edition). lecture notes for linear algebra gilbert strang pdf
Convert the whiteboard drawings into clean, digital diagrams.
His four fundamental subspaces (column space, nullspace, row space, and left nullspace) tie the entire subject together. Standard textbooks often obscure this beauty. Strang’s lecture notes, however, illuminate it. The journey begins with solving simultaneous equations
This part focuses on the mechanics of solving square systems of linear equations. You'll master Gaussian elimination, the LU decomposition, and the concept of matrix inverses. Strang also explains how to analyze whether a solution exists and whether it is unique using the rank of the matrix.
She printed a single page and smoothed it on the dorm desk. Row reduction marched across the sheet like soldiers in neat columns. The proofs felt like instructions from a craftsman: precise, honest, designed to make curious hands capable. Elena circled a line about eigenvectors being directions that don’t change, and smiled. It sounded like the kind of truth you could carry through bad days. Professor Strang maintains a personal MIT faculty page
| Aspect | Official Lecture Notes (MIT OCW) | Textbook (Strang) | | :--- | :--- | :--- | | | ✅ Yes, free | ❌ No (publisher-controlled) | | Depth | Concise (1–2 pp/lecture) | Comprehensive (600+ pp) | | Exercises | A few per topic | Hundreds with answers | | Applications | Minimal | Rich (engineering, CS, economics) | | Best for | Review, exam prep, video companion | Self-contained course learning |
Beyond the free OCW handouts, several structured PDF and ebook options exist for more in-depth study:
For older editions (e.g., Strang’s 3rd and 4th editions of Introduction to Linear Algebra ), the Internet Archive (archive.org) sometimes holds borrowable digital copies of the lecture notes prepared by teaching assistants. While you cannot "download" these permanently, you can read them online legally.
If you prefer to learn from a textbook rather than lecture notes, any of these are fantastic options.