Lecture notes:

Lecture 1 - Introduction

Lecture 2 - The Algebra of Matrices

Lecture 3 - Gaussian Elimination

Lecture 4 - Homogeneous Systems

Lecture 5 - Matrix Multiplication

Lecture 6 - Matrix Products: Applications

Lecture 7 - Matrix Inverses

Lecture 8 - Inverses and Elementary Matrices

Lecture 9 - Markov Chains

Lecture 10 - Determinants

Lecture 11 - Determinants: Properties

Lecture 12 - Adjoints

Lecture 13 - The Eigenvalue Problem

Lecture 14 - Diagonaliztion

Lecture 15 - Similar Matrices and Complex Numbers

Lecture 16 - Complex Eignevalues

Lecture 17 - Linear Recurrences

Lecture 18 - Vectors

Lecture 19 - Dot Products

Lecture 20 - Projections

Lecture 21 - Lines

Lecture 22 - Planes

Lecture 23 - Linear Transformations

Lecture 24 - The Cross Product

Lecture 25 - Subspaces

Lecture 26 - Linear Independence

Lecture 27 - Bases

Lecture 28 - Dimension

Lecture 29 - Rank

Lecture 30 - Full Rank

Lecture 31 - Orthogonality

Lecture 32 - The Gram-Schmidt Algorithm