EE 2100 Matrix Theory

Welcome to the official webpage of the course EE2100 (Matrix Theory).

This course is primarily targeted for undergraduate students. Matrix Theory can be taught in several ways and has applications in several domains. This course aims to introduce linear algebra concepts and look at their applications in various disciplines (mainly from Electrical Engineering and a few from Machine Learning).

Course Contents : Introduction to vectors, elementary operations on vectors, Dot product, Norm of a vector, Caucy-Schwarz inequality, Projection, Vector Space, Subspace, Linear Combination, Span, Linear independence, Spanning Set, Basis, Orthogonal basis, representation of a vector in orthogonal basis, Graham Schmidt Algorithm, projection of a vector onto subspace, K-means Clustering, Introduction to Matrices, Matrix-Vector Product, Linear Transformations, Inverse of a Matrix, Matrix Multiplication, Fundamental Subspaces of Matrix, System of Linear Equations, Rank-Nullity Theorem, Gaussian Elimination, LU decomposition, Overdetermined System of Linear Equations, Linear Regression, Trace of a matrix, Determinant of a matrix, Eigen Values and Eigen Vectors, Spectral Theorem, Rayleigh quotient, Quadratic Forms, Positive Definite matrices, Positive semidefinite matrices, Cholesky decomposition, QR decomposition, Singular value decomposition (SVD), Matrix Norms and Principal component Analysis.

The objective of the course is to explore applications associated with the concepts covered in this course. A few applications are covered in the main lecture, while a few others are first introduced as a part of the assignment. In cases where the applications are covered as a part of the assignment, a supplementary material/tutorial is provided to give sufficient background related to the application. Post the assignment deadline, the application areas are extensively reviewed.

Applications covered: Convolution, Discrete Fourier Transform, Role of Matrices in Circuits, Clustering (k-means), Linear Regression, Polynomial regression in one variable, Role of matrices in Graphs, Numerical solution to differential equations

Instructor

• Name : Seshadri Sravan Kumar V

• Email : seshadri@ee.iith.ac.in

• Office : 534, Academic Block C

Class Timings

• Class timings : Slot C (Monday 11:00 - 11:55, Wednesday 10:00 - 10:55 and Thursday 09:00 - 09:55)

• Venue: LH1, Academic Block A

Evaluation Pattern

• Assignments : 25% (Top 8 scores will be considered)

• Quizzes : 30% (Top 5 scores will be considered)

• Exams : 45% (20% for Mid-Term and 25% for Final Exam)

References

• Gilbert Starng, “Linear Algebra and its applications”, Cengage Learning

• S H FriedBerg, A J Insel, L E Spence, “Linear Algebra”, PHI Learning

• S Boyd and L Vandenberghe, “Introduction to Applied Linear Algebra”, Cambridge university press [ebook available on Prof. Boyd’s Webpage]

• E Kreyszig, “Advanced Engineering Mathematics”, Wiley.

• M Greenberg, “Advanced Engineering Mathematics”, Pearson

Teaching Assistants

Credit to the following undergraduate students who have volunteered to serve as Teaching Assistants for the course.