Lecture Notes For Linear Algebra Gilbert Strang Jun 2026

Strang organizes the universe of a matrix $A$ into four distinct subspaces: the Column Space and the Nullspace (for the row world), and the Row Space and the Left Nullspace (for the column world). The deep insight delivered in these lectures is the concept of orthogonality not just as a geometric quirk, but as a structural necessity.

Vectors (v) and (w) are orthogonal if (v^Tw = 0). Two subspaces are orthogonal if every vector in one is orthogonal to every vector in the other. lecture notes for linear algebra gilbert strang

Dot product, projections, Gram-Schmidt, QR factorization, least squares. Strang organizes the universe of a matrix $A$

: Don't just read the notes; watch the 18.06 lectures on YouTube or MIT OCW. Strang’s chalkboard style is designed for you to follow along in real-time. lecture notes for linear algebra gilbert strang