MATH 3120 — Linear Algebra

UPenn MATH 3120, Spring 2026.
Course website

daniel.krashen+lalg@gmail.com

Lecture 1 (January 14, 2026): Introductions

Lecture 2 (January 21, 2026): Reduced row echelon form, spaces of vectors

Lecture 3 (January 28, 2026): Rank and number of solutions, introduction to matrix algebra

Lecture 4 (February 2, 2026): Matrix algebra

Lecture 5 (February 4, 2026): Linear transformations and matrices

Lecture 6 (February 9, 2026): Matrix multiplication is composition, intro to matrix factorization

Lecture 7 (February 11, 2026): Matrix factorization, subspaces, image, rank, nullity

Lecture 8 (February 16, 2026): Spanning and independent sets, geometry and projections

Exam 1 practice sheet (February 18, 2026):

Lecture 9 (March 2, 2026): More orthogonality, introduction to determinants

Lecture 10 (March 4, 2026): Determinants, transposes

Lecture 11 (March 16, 2026): Determinants, abstract vector spaces

Lecture 12 (March 18, 2026): Linear transformations between abstract vector spaces, isomorphisms, inner products

Lecture 13 (March 23, 2026): Least squares approximations and applications

Exam 2 practice sheet (February 18, 2026):

Lecture 14 (April 1, 2026): Rank-nullity, matrices from linear transformations

Lecture 15 (April 6, 2026): Eigenvalues and eigenvectors

Lecture 16 (April 8, 2026): Symmetric matrices have real eigenvalues

Lecture 17 (April 13, 2026): The (real) spectral theorem / principal axes theorem

Lecture 18 (April 15, 2026): Worksheet practice (#7)

Lecture 19 (April 19, 2026): Singular value decomposition