Instructor: Simerdeep Singh

In this course, we will cover finite-dimensional vector spaces, subspaces, span of vectors, bases, linear maps, eigenvalues, eigenvectors, inner product spaces, and many more topics. Although the course covers material for an arbitrary field and an arbitrary finite-dimensional vector space, it makes an extra effort to emphasize concepts and examples from Rn vector spaces, and vector spaces containing matrices. This will make sure that the students after completing this course know linear algebra both from an abstract perspective and from the perspective of its highly specific popular form, the matrix algebra. Many of you who think that linear algebra is all about matrices will realize that it is not the case. A matrix vector space is one type of finite-dimensional vector space, and linear algebra is the study of an arbitrary finite-dimensional vector space. Upon completion of the entire series: Linear Algebra I, II, and III, we recommend taking Matrix Algebra that covers advanced topics such as determinants, linear systems, and derivatives involving matrices. All this will lay a strong mathematical foundation for machine learning courses, statistics, and advanced courses in physics.