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:

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

Course Outcomes:

After completing this course, students should be able to:
CO1: Apply proximal algorithms, augmented Lagrangian, and ADMM to solve convex and non-convex optimization problems.
CO2: Develop optimization algorithms used in neural networks.
CO3: Apply statistical estimation theory and hypothesis testing to data analysis applications.
CO4: Apply quantum computing concepts to solve problems in various fields including cryptography and optimization.

CO-PO Mapping

• 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).
• Larry Wasserman. All of Statistics: A Concise Course in Statistical Inference (Springer Texts in Statistics, 2003).