My notes for when I took this course in Summer 2025, taught by Alex Burka through Axler’s Linear Algebra Done Right, 4th edition.

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Please submit any errors you might find in the errata, thank you!

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Phoenix Wilson

Course by Week

Week Topics
1 Functions, Fields, Vector Spaces, Span, Linear Independence, Basis, Dimension
2 Linear Maps, Linear Isomorphisms, Coordinates, Matrices
3 Gaussian Elimination, Change of Basis, Dual Spaces, Dual Maps, Polynomials
4 Invariant Subspaces, Eigenstuff, Minimal Polynomial
5 Upper-Triangularizability, Diagonalizability
6 Generalized Eigenstuff, Jordan Form, Inner Product Spaces, Gram-Schmidt, Orthogonal Complements, Projections
7 Riesz Representation Theorem, Adjoints, Spectral Theorem

Functions, Fields, Vector Spaces, Span, Linear Independence, Basis, Dimension

Linear Maps, Linear Isomorphisms, Coordinates, Matrices

Gaussian Elimination, Change of Basis, Dual Spaces, Dual Maps, Polynomials

Invariant Subspaces, Eigenstuff, Minimal Polynomial

Upper-Triangularizability, Diagonalizability

Generalized Eigenstuff, Jordan Form, Inner Product Spaces, Gram-Schmidt, Orthogonal Complements, Projections

Riesz Representation Theorem, Adjoints, Spectral Theorem

Special Topics

These are topics I self-studied after the course concluded.

Chapter Topics
7 Positive, Unitary, Isometries
Singular Value Decomposition
9

Positive, Unitary, Isometries

Singular Value Decomposition