Linear algebra is a branch of mathematics that lies at the heart of applied science and engineering. This is an intermediate linear algebra course aimed at a diverse group of students, including undergraduates in applied mathematics, information and data sciences, and engineering, as well as graduate students in science and engineering. The main goal of the course is to provide an introduction to the fundamental ideas, concepts, and methods of applied linear algebra and illustrate them with important applications.

Topics covered include linear systems; PLU factorization; vector spaces and bases; fundamental matrix subspaces; inner products; norms; Cauchy–Schwarz and triangle inequalities; normed spaces; k-means algorithm; positive-definite and Gram matrices; least squares solutions; weighted least squares; polynomial interpolation; orthogonal projections; Gram–Schmidt process; QR factorization; Legendre polynomials; polynomial approximation; eigenvalues, eigenvectors and eigenbases; Gershgorin’s theorem; Perron’s theorem; PageRank algorithm; power method; diagonalization; symmetric matrices, spectral theorem, optimization interpretation of eigenvalues and eigenvectors; singular values and singular vectors; singular value decomposition; condition number; pseudoinverse; matrix norms; best rank-k approximation; Eckart–Young theorem; and applications to clustering, text classification, data fitting, ranking webpages, principal component analysis, spectral method for graph partitioning, image compression, political science, and facial recognition.

• Ma 1 abc (enforced prerequisite).
• Some familiarity with MATLAB, e.g. ACM 11, is desired.

Each lecture will be accompanied by two practice problems: a somewhat easier, more practical Problem A, and a more difficult, more conceptual Problem B. The main goal of the practice problems is threefold: to help you better understand the material covered in the corresponding lecture, to help you prepare to solve problems in problem sets and exams, and to accommodate the diversity of students’ math backgrounds by providing both easier and more challenging problems. These problems are for self-practice: they will not be graded, and the solutions (posted on Piazza) also illustrate the expected level of rigor for problem sets and exams.

There will be six Problem Sets. Problems (and solutions) will be posted on Piazza. For assignment and due dates see “Important Dates” below. Late submissions will not be accepted for any reason, but the Problem Set with the lowest score will be dropped and not counted toward your total score. Submitting wrong files or files in a wrong format is considered as a late submission. Extensions may be granted for academic, personal, or medical reasons. For extensions, please email the Head TA.

Your final grade will be based on your total score. Your total score is a weighted average of Problem Sets (50%), Midterm Exam (10%), and Final Exam (40%). You can increase your total score by up to 5% if you participate actively in Piazza discussions in the Q&A section. Each student answer that is submitted before a TA or the instructor posts an answer, and that is later endorsed as a ‘good answer’ by a TA or the instructor, adds 1% to your total score. There are no fixed thresholds for grades, but if your total score is 90% (80%, 70%, 60%), then you are guaranteed at least A (B, C, D).