Linear Algebra For Data Science

21-670 Linear Algebra For Data Science

Fall 2021 (Mini-1)

Class Info

Class time: MWF 9:05am - 9:55am
Class location: WEH 7201
Office Hours (online!): Tuesday 10:30am - noon; Thursday 10:00am - 11:30am

Textbook

There is no official textbook for the class. However, I will be following the first part of Gilbert Strang's Linear Algebra and Learning From Data for the first four weeks. Trefethen and Bau's Numerical Linear Algebra will be a secondary source. For the material on tensors, I will be drawing from Chapter 12 of Matrix Computations by Golub.

Course Description

This course is designed to present and discuss those aspects of linear algebra that are most important in data analytics. The emphasis will be on developing intuition and understanding how to use linear algebra, rather than on proofs. The main topics include:

Basic matrix operations, linear transformations
Subspaces, ranges and null spaces, linear combinations and spans, linear independence, bases, dimension, rank and nullity theorem
Systems of linear equations, symmetric matrices, inverses, determinants, triangular matrices, trace, eigenvalues and eigenvectors
Positive definite matrices, covariance matrices, minimization problems involving matrices, minimization and convex functions.
Orthogonal projections, Gram-Schmidt procedure, singular value decomposition
Tensor structures and tensor trains

Although this course is required for all students enrolled in the MS in Data Analytics for Science program, it is intended for students with a less solid mathematical preparation.

Grading

There will be 4-5 homework assignments and a final exam.

Resubmitting Homework: After HWs are graded and returned, you may correct and resubmit problems on which you missed points (please send to my e-mail). I will accept re-submitted problems until the day of the final (Oct. 14).

Assignments are weighted as follows in the final grade computation:

Homework (75%)
Final (25%)

Letter grade cutoffs will be determined at the end of the semester, but will not be more harsh than the standard cutoffs of 90% - 100% = A, 80% - 89.9% = B, etc.