Course11110711240 lectures
Matrix Analysis with Applications
Prof. S. K. Gupta and Prof. Sanjeev Kumar · IIT Roorkee
About
This course is offered to UG and PG students of Engineering/Science background. It contains the concepts related to matrix theory and their applications in various disciplines. It covers a depth understanding of matrix computations involving rank, eigenvalues, eigenvectors, linear transformation, similarity transformations, (diagonalisation, Jordan canonical form, etc). It also involves various iterative methods, including Krylov subspace methods. Finally, topics like positive matrices, non-negative matrices and polar decomposition are discussed in detail with their applications.
Intended audience: UG and PG students of technical universities/colleges
Lectures
Week 1
- Elementary row operations
- Echelon form of a matrix
- Rank of a matrix
- System of Linear Equations-I
- System of Linear Equations-II
Week 2
Week 3
- Inverse of a Linear Transformation
- Matrix Associated with a LT
- Eigenvalues and Eigenvectors
- Cayley-Hamilton Theorem and Minimal Polynomial
- Diagonalization
Week 4
- Special Matrices
- More on Special Matrices and Gerschgorin Theorem
- Inner Product Spaces
- Vector and Matrix Norms
- Gram Schmidt Process
Week 5
- Normal Matrices
- Positive Definite Matrices
- Positive Definite and Quadratic Forms
- Gram Matrix and Minimization of Quadratic Forms
- Generalized Eigenvectors and Jordan Canonical Form
Week 6
- Evaluation of Matrix Functions
- Least Square Approximation
- Singular Value Decomposition
- Pseudo-Inverse and SVD
- Introduction to Ill-Conditioned Systems
Week 7
- Regularization of Ill-Conditioned Systems
- Linear Systems : Iterative Methods I
- Linear Systems : Iterative Methods II
- Non-Stationary Iterative Methods: Steepest Descent-I
- Non-Stationary Iterative Methods: Steepest Descent-II
Week 8
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Roorkee
- Department
- Mathematics
- Taught by
- Prof. S. K. Gupta, Prof. Sanjeev Kumar
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed