Basics of Linear Algebra – Linear Dependence and independence of vectors – Gaussian Elimination – Rank of set of vectors forming a matrix – Vector space and Basis set for a Vector space – Dot product and Orthogonality – Rotation matrices – Eigenvalues and Eigenvectors and its interpretation – Projection matrix and Regression – Singular Value Decomposition.

Convolution sum, Convolution Integral, Ordinary Linear differential equations, formulation, analytical and Numerical solutions, Impulse Response Computations, formulating state space models of Physical systems.

Examples of ODE modelling in falling objects, satellite and planetary motion, Electrical and mechanical systems. Multivariate calculus, Taylor series, Introduction to Optimization.

Introduction to Probability Distributions and Monte Carlo Simulations.

Course Objectives

The course will lay down the basic concepts and techniques of linear algebras applied to signal processing. It will explore the concepts initially through computational experiments and then try to understand the concepts/theory behind it. At the same time, it will provide an appreciation of the wide application of these disciplines within the scientific field. Another goal of the course is to provide connection between the concepts of linear algebra, differential equation and probability theory.

Course Outcomes

Course Evaluation Pattern:

Internal – 75%

• Assignments – 50% (20 assignments with equal credit)
• Quiz- 25% (5 Quizzes with equal credit)

External – 25%

• Project – 25%

1. Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019.
2. William Flannery, Mathematical Modelling and Computational Calculus, Vol-1, Berkeley Science Books, 2013.