Course

Unit 1

Special Matrices: Fourier Transform, discrete and Continuous, Shift matrices and Circulant matrices, The Kronecker product, Toeplitz matrices and shift invariant filters, Hankel matrices, DMD and need of Hankelization – Importance of Hankelization – DMD and its variants – Linear algebra for AI 

Unit 2

Matrix splitting and Proximal algorithms – Augmented Lagrangian- Introduction to ADMM, ADMM for LP and QP – Optimization methods for Neural Networks: Gradient Descent, Stochastic gradient descent- loss functions and learning functions 

Unit 3

Basics of statistical estimation theory and testing of hypothesis.

Unit 4

Introduction to quantum computing- Bells’s circuit, Superdense coding, Quantum teleportation. Programming using Qiskit, Matlab.

Course Objectives

• To provide students with advanced knowledge and skills in optimization, statistical estimation theory, and quantum computing.
• To understand and analyze special matrices used in various areas of signal processing and data analysis.
• To learn optimization techniques for convex and non-convex problems, and their application to machine learning problems. 
• To introduce statistical estimation theory and hypothesis testing, and their relevance to data analysis. 
• To provide an overview of quantum computing and its potential applications in various field 

Course Outcomes

After completing this course, students will be able to

CO-PO Mapping

Evaluation Pattern 

Text Books / References

Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019. 

Gilbert Strang, “Differential Equations and Linear Algebra Wellesley”, Cambridge press, 2018. 

Stephen Boyd and, Lieven Vandenberghe, “Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares”, Cambridge University Press, 2018 

Bernhardt, Chris.?Quantum computing for everyone. Mit Press, 2019. (From pages 71 to 140).