18.700 - Linear Algebra (Fall 2024)

Schedule

The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.

Unless otherwise noted, indicated sections refer to the textbook Linear Algebra Done Right by Axler. [B] refers to A First Course in Linear Algebra by Rob Beezer, and [LADW] refers to Linear Algebra Done Wrong by Sergei Treil.

Semester Timeline
Date Sections in Text Description Notes
(W) Sep 4 [B], Ch. 1,
[LADW], Ch. 2
Linear systems Lecture 1
Worksheet 1
Row reduction slides
(M) Sep 9 [B], Ch. 1,
[LADW], Ch. 2
Gaussian elimination Lecture 2
Row reduction SageMathCell
(W) Sep 11 1A, 1B RR^n, CC^n, Vector spaces Lecture 3
Worksheet 3
(M) Sep 16 1C Subspaces, Direct sums Lecture 4
(W) Sep 18 2A Span, Linear independence Lecture 5
Worksheet 5
(M) Sep 23 2B, 2C Bases, Dimension Lecture 6
(W) Sep 25 3A, 3B Linear maps, Null space, Range Lecture 7
Worksheet 7
(M) Sep 30 3C Matrices Lecture 8
(W) Oct 2 3D Invertibility, Isomorphisms Lecture 9
(M) Oct 7 5A Invariant subspaces, Eigenvectors Lecture 10
Worksheet 10
(T) Oct 8 Review session for Exam 1, 7 - 9 pm, Room 2-361
(W) Oct 9 Exam 1 on Ch. 1 - 3 Exam 1 review packet
(M) Oct 14 Indigenous Peoples Day, no class
(W) Oct 16 5B Minimal polynomial Lecture 11
(M) Oct 21 5C, 5D Upper triangular matrices, Diagonalization Lecture 12
(W) Oct 23 5D Diagonalization Lecture 13
Worksheet 13
(M) Oct 28 6A, 6B Inner products and norms
Orthonormal bases and Gram-Schmidt
Lecture 14
(W) Oct 30 6C Orthogonal complements, Minimization Lecture 15
Worksheet 15
Worksheet 15 Solutions
(M) Nov 4 7A Adjoint, Self-Adjoint, and Normal Operators Lecture 16
(W) Nov 6 7B Spectral theorem Lecture 17
(M) Nov 11 Veterans Day, no class
(T) Nov 12 Review session for Exam 2, 7 - 9 pm, Room 2-361
(W) Nov 13 Exam 2 on Ch. 1 - 6 Exam 2 review packet
(M) Nov 18 7C, 7D Positive operators, Isometries and matrix factorizations Lecture 18
(W) Nov 20 7E, 7F Singular value decomposition
Drop date
Lecture 19
Worksheet 19
(M) Nov 25 8A Generalized eigenvectors Lecture 20
(W) Nov 27 8B Generalized eigenspace decomposition Lecture 21
(M) Dec 2 8C, 8D Jordan canonical form, Trace Lecture 22
Worksheet 22
(W) Dec 4 9A, 9B Bilinear and multilinear forms Lecture 23
(M) Dec 9 9C Determinants Lecture 24
3Blue1Brown video
(W) Dec 11 Determinants and Review
(F) Dec 13 Review session for Final Exam, 7 - 9 pm, Room 2-361
(M) Dec 16
Final Exam: 1:30 - 4:30 pm,
Room 6-120
Final Exam practice