Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Dr. Sanjeev Kumar, S. K. Gupta
NPTEL Co-ordinating Institute : IIT Roorkee
NPTEL Lecture Count : 40
NPTEL Course Size : 5.4 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Elementary row operations
Lecture 2 - Echelon form of a matrix
Lecture 3 - Rank of a matrix
Lecture 4 - System of Linear Equations - I
Lecture 5 - System of Linear Equations - II
Lecture 6 - Introduction to Vector Spaces
Lecture 7 - Subspaces
Lecture 8 - Basis and Dimension
Lecture 9 - Linear Transformations
Lecture 10 - Rank and Nullity
Lecture 11 - Inverse of a Linear Transformation
Lecture 12 - Matrix Associated with a LT
Lecture 13 - Eigenvalues and Eigenvectors
Lecture 14 - Cayley-Hamilton Theorem and Minimal Polynomial
Lecture 15 - Diagonalization
Lecture 16 - Special Matrices
Lecture 17 - More on Special Matrices and Gerschgorin Theorem
Lecture 18 - Inner Product Spaces
Lecture 19 - Vector and Matrix Norms
Lecture 20 - Gram Schmidt Process
Lecture 21 - Normal Matrices
Lecture 22 - Positive Definite Matrices
Lecture 23 - Positive Definite and Quadratic Forms
Lecture 24 - Gram Matrix and Minimization of Quadratic Forms
Lecture 25 - Generalized Eigenvectors and Jordan Canonical Form
Lecture 26 - Evaluation of Matrix Functions
Lecture 27 - Least Square Approximation
Lecture 28 - Singular Value Decomposition
Lecture 29 - Pseudo-Inverse and SVD
Lecture 30 - Introduction to Ill-Conditioned Systems
Lecture 31 - Regularization of Ill-Conditioned Systems
Lecture 32 - Linear Systems: Iterative Methods - I
Lecture 33 - Linear Systems: Iterative Methods - II
Lecture 34 - Non-Stationary Iterative Methods: Steepest Descent - I
Lecture 35 - Non-Stationary Iterative Methods: Steepest Descent - II
Lecture 36 - Krylov Subspace Iterative Methods (Conjugate Gradient Method)
Lecture 37 - Krylov Subspace Iterative Methods (CG and Pre-Conditioning)
Lecture 38 - Introduction to Positive Matrices
Lecture 39 - Positive Matrices, Positive Eigenpair, Perron Root and vector, Example
Lecture 40 - Polar Decomposition