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Introduction to Linear Algebra

The classic foundation of linear algebra, from geometry and elimination to SVD and data science.

Gilbert Strang, 2023. Wellesley-Cambridge Press

What is actually freeMIT and the author publish the Table of Contents, selected sample sections, typos/errata, and solution sets freely online on MIT Mathematics. Fully free as well is MIT 18.06 (Linear Algebra), the complete course taught by Professor Strang with 34 recorded video lectures, transcripts, and problem sets. Every link here connects directly to MIT OpenCourseWare and official MIT servers.

What is free, section by section39 sections
Full chapter, free to read: 0 of 39 sectionsCovered by a lecture: 39 of 39 sectionsProblem set and contents only: 0 of 39 sections
  • Full chapter, free to read 0
  • Covered by a lecture 39
  • Problem set and contents only 0

Most of this book is followed through the lectures rather than the page. That is the honest shape of what MIT publishes, and it is why the roadmap is built around the course rather than around chapter downloads.

Vectors and Matrices

Vectors, linear combinations, dot products, angles, and matrix-vector multiplication.

Part 1 progress: 0/4 sections read

Before moving on from Part 1

Solving Linear Equations Ax = b

Gaussian elimination, elimination matrices, matrix inverses, and LU factorization.

Part 2 progress: 0/5 sections read

Before moving on from Part 2

The Four Fundamental Subspaces

Vector spaces, column space, nullspace, independence, basis, dimension, and the Fundamental Theorem.

Part 3 progress: 0/5 sections read

Before moving on from Part 3

Orthogonality

Orthogonal subspaces, projection matrices, least squares regression, and the Gram-Schmidt process.

Part 4 progress: 0/4 sections read

Before moving on from Part 4

Determinants

Pivot formulas, cofactor expansions, Cramer's rule, and geometric volumes.

Part 5 progress: 0/3 sections read

Before moving on from Part 5

Eigenvalues and Eigenvectors

Diagonalization, system of differential equations, symmetric positive definite matrices, and complex matrices.

Part 6 progress: 0/5 sections read

Before moving on from Part 6

The Singular Value Decomposition (SVD)

Singular values and singular vectors, low-rank matrix approximations, image compression, and PCA.

Part 7 progress: 0/3 sections read

Before moving on from Part 7

Linear Transformations

Linear mappings, the matrix of a transformation, and change of basis.

Part 8 progress: 0/3 sections read

Before moving on from Part 8

Linear Algebra in Optimization

Multivariable minimization, gradient descent, backpropagation, and linear programming duality.

Part 9 progress: 0/4 sections read

Before moving on from Part 9

Learning from Data

Piecewise linear learning functions, deep neural network architecture, and covariance matrices.

Part 10 progress: 0/3 sections read

Before moving on from Part 10

Material for the whole book

Official Book Page, from Gilbert Strang / MIT, opens in a new tab

MIT 18.06 Course on OCW, from MIT OpenCourseWare, opens in a new tab

All 34 Video Lectures, from MIT OpenCourseWare / YouTube, opens in a new tab

Wellesley-Cambridge Press, from Wellesley-Cambridge Press, opens in a new tab

Attribution

Introduction to Linear Algebra is copyright 2023 Gilbert Strang, published by Wellesley-Cambridge Press. This page is an independent reading guide. It reproduces no part of the book and hosts no files: every link above points to the author's own page or to the publishing university's servers.

Lecture and problem links go to MIT 18.06, Linear Algebra (Spring 2010), used under CC BY-NC-SA 4.0.

If this book is useful to you and you can afford it, buy a copy. That is what keeps authors writing them.