Vectors | Chapter 1, Essence of linear algebra

Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra

Linear transformations and matrices | Chapter 3, Essence of linear algebra

Matrix multiplication as composition | Chapter 4, Essence of linear algebra

Three-dimensional linear transformations | Chapter 5, Essence of linear algebra

The determinant | Chapter 6, Essence of linear algebra

Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra

Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra

Dot products and duality | Chapter 9, Essence of linear algebra

Cross products | Chapter 10, Essence of linear algebra

Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra

Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra

Change of basis | Chapter 13, Essence of linear algebra

Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra

A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra

Abstract vector spaces | Chapter 16, Essence of linear algebra