Course title: Applied Linear Algebra
Lecture hours: 3
Tutorial hour(s): 1
Typical Slot: D
Description:
Real-world systems or scenarios throw at us lot of information which needs to be understood and processed. This analysis becomes easier when the available information is organised in a certain structure, which makes it easier to understand the underlying information in a better way. This course on Linear Algebra provides us with mathematical abstractions and structures to organize, analyze and interpret information and is one of the fundamental tools in any engineering studies. The course will start with an introduction to vector spaces and subspaces, linear functions, systems of linear equations, matrices as linear transformations, matrix algebra, with engineering applications.
Course content:
- What is Linear Algebra: Vectors, dot products, linear combinations, linear functions, Matrices.
- Systems of Linear Equations: Gaussian elimination, Elementary row operations
- Vector spaces and subspaces: Spaces of vectors, span, basis, linear independence, dimension, rank nullity theorem, four fundamental subspaces, change of basis, complete solution to a system of linear equations, orthonormal bases.
- Matrices: Eigenvalues and Eigenvectors, Diagonalisation of matrices, Symmetric matrices, Positive definite matrices, generalized Eigenvectors, Jordan form, Singular value decomposition.
- Linear transformation, matrix representation of a linear transformation.
- Applications: Image processing, Optimisation, Networks,
Prerequisite: None
Books:
- K. Janich. Linear Algebra. Springer. 1994.
- H. Anton. C. Rorres. Elementary Linear Algebra: Applications, Wiley; 11th edition, 2013
Previous Instance of the course:
- 2025,2024 (July-Nov; Dr. Lakshmi Narasimhan Theagarajan)