E0 299: Computational Linear Algebra
Announcements:
Registration is strictly restricted to MTech (AI) 2020-2022. (others are welcome to audit).
The first online meeting is on October 1 from 3:30 - 4:30 pm.
The final exam is on January 30, 10:00-13:00 hrs.
Course Details
Term: October 2020 - January 2021.
Credits: 3:1.
Webpage: https://tinyurl.com/CompLinAlg
Hours: Wednesday, Friday: 5:00 - 6:30 pm.
Instructor: Kunal N. Chaudhury (kunal@iisc.ac.in).
Teaching Assistants: Ruturaj Gavaskar, Pravin Nair, Unni VS, Tripti Jain.
Grading: math problems (15%), coding assignments (15%), continuous assessment/tests (40%), final exam (30%).
Objective: To provide a good mix of geometric intuition, theorem proving, and how things can be computed efficiently. This is really an introductory course on linear algebra with a focus on theory, but we will also touch upon some algorithmic aspects without getting into details (coding assignments will be given in this regard).
Syllabus:
Theory: Solution of linear equations, vector space, linear transformations, matrix representation, inner-products and norms, orthogonality and least-squares, trace and determinant, eigendecomposition, symmetric (Hermitian) matrices and quadratic forms, singular value decomposition.
Computations: linear solvers, least squares, QR (Gram-Schmidt), SVD.
Textbooks:
S. Axler, Linear Algebra Done Right, Springer, 2015.
G. Strang, Linear Algebra and its Applications, Brooks/Cole, 2006.
L. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.
Web resources:
http://ocw.mit.edu/18-06S05 (video lectures by Strang)
http://vmls-book.stanford.edu/ (linear algebra applications)
http://immersivemath.com/ila/index.html (nice visualizations)
https://math.stackexchange.com/?tags=linear-algebra (lots of Q/A)