These 15 lessons are intended as an outline for an undergraduate Mathematics course on Linear Algebra, or as revision notes for a student undertaking such a course.
The format is GFM-compatible, suitable for importing as sources into NotebookLM.
The content is believed to be complete and correct, however detailed technical review has not been carried out. Feel free to raise issues to make corrections or improvements, or submit pull requests.
- Vectors and Linear Combinations
- Solving Linear Equations by Elimination
- Matrix Algebra and LU Factorisation
- Vector Spaces and the Nullspace
- Rank, Dimension, and the Four Subspaces
- Orthogonality of Vectors and Subspaces
- Projections and Least Squares
- Determinants and Cramer's Rule
- Eigenvalues and Eigenvectors
- Symmetric Matrices and Differential Equations
- The Singular Value Decomposition (SVD)
- Applications of SVD—PCA and Compression
- Linear Transformations and Change of Basis
- Linear Algebra in Optimisation
- Learning from Data
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1.00 2025-01-13: Initial release, word count 13466.