Matrix Theory / Jul-Nov 2026

Course Description

This course develops a rigorous and intuitive understanding of linear algebra, emphasizing both mathematical foundations and applications in artificial intelligence. Students will study vectors, matrices, linear transformations, subspaces, orthogonality, eigenvalues, and matrix factorizations through geometric, algebraic, and computational viewpoints. The course will connect theory with machine learning, data analysis, optimization, signal processing, and representation learning. Particular attention will be given to reasoning, proof, problem formulation, and the interpretation of high-dimensional spaces. By the end of the course, students should be able to analyze linear systems, understand the structure of linear operators, and apply linear algebra confidently to modern AI problems.

(AI1000) Matrix Theory Course Contents

Systems of linear equations; row and column viewpoints; Gaussian elimination; matrix operations; inverses; vector spaces, subspaces, span, linear independence, basis, dimension, rank, and null spaces; linear transformations and matrix representations; determinants and their geometric interpretation; inner products, norms, orthogonality, projections, Gram–Schmidt orthogonalization, and least-squares problems; eigenvalues, eigenvectors, diagonalization, and spectral decomposition; symmetric, orthogonal, positive definite, and positive semidefinite matrices; singular value decomposition and low-rank approximation; Applications and carefully selected examples from modern machine learning and deep learning.

Logistics

Class Room: TBA

Timings: Slot-D

Visit this page regularly for updates and information regarding the course.

Instructors

Dr Konda Reddy Mopuri

Teaching Assistants