Matrix Theory / Jul-Nov 2026
Updates
- Aug 17: New Lecture is up: (MT-08) Complete solution to Ax=b
- Aug 14: New Lecture is up: (MT-07) Column Space and Null Space [Slides] [Annotated-slides]
- Aug 14: New Lecture is up: (MT-06) Vector Spaces and Subspaces [Slides]
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Aug 07, 2026: Quiz-1 on 11th Aug, 8.30 - 10 AM (LHC-1).
Syllabus: System of linear equations (row and column picture), Gaussian Elimination, LU decomposition, basics on inverse and transpose of a matrix.
- Aug 07: New Lecture is up: (MT-03) Transpose of a Matrix [Notes]
- Aug 04: New Lecture is up: (MT-04) Inverse of a Matrix [Notes]
- Aug 03: New Lecture is up: (MT-03) Triangular Factorization [slides] [Annotated-slides]
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.
