Instructor: Sungwoong Kim
Time: Fri 14:00 - 16:45 (15:15 - 15:30, break time)
Room: Science & Engineering Library 611
Contact: swkim01@korea.ac.kr or blackboard
Linear algebra is one of the fundamental mathematics fields that tries to solve linear equations through the manipulation of vectors and matrices. Especially, main techniques in linear algebra such as the vectorization, matrix factorization, and linear mapping are widely used in machine learning and deep learning. For example, vector and matrix operations are core factors for parallelization of deep neural network processing, and matrix factorizations (decompositions) are popularly used for approximating the structured matrices to efficiently reduce numerical precisions or enable fast computations. More importantly, structured modeling is the core of machine learning and deep learning, and vectors and matrices in linear algebra can basically represent this structured modeling (e.g. image). This course will first review the basic concepts and operations of linear algebra, and then introduce some popular techniques that are useful in solving machine learning problems.
The course will cover the basic concepts and key factors in linear algebra such as vector spaces, matrix decompositions, and linear mappings. In addition, the course will introduce how these techniques are related and applied for machine learning and deep learning, especially from an optimization perspective. From the course, students would have enough knowledge and good intuition regarding linear algebra and its applications to machine learning.
Basic knowledges in calculus, optimization, machine learning, and deep learning are preferred but not required.
Lecture notes will be the main material of the course, and these do not come from a single textbook. However, the lecture notes will be mainly based on the following two textbooks.
Gilbert Strang, Introduction to Linear Algebra, Sixth Edition, 2023.
Gilbert Strang, Lecture Notes for Linear Algebra, 2021.
Attendance (20%)
Midterm exam (40%)
Final exam (40%)