Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Swanand Khare
NPTEL Co-ordinating Institute : IIT Kharagpur
NPTEL Lecture Count : 60
NPTEL Course Size : 3.9 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Vector Spaces
Lecture 2 - Vector Subspaces
Lecture 3 - Linear Span and Linear Dependence
Lecture 4 - Linear Independence
Lecture 5 - Basis and Dimension
Lecture 6 - Linear Functionals
Lecture 7 - Norm of Vector - Part I
Lecture 8 - Norm of Vector - Part II
Lecture 9 - Linear Functions
Lecture 10 - Affine Functions and Examples
Lecture 11 - Examples of Linear and Affine Functions
Lecture 12 - Function Composition
Lecture 13 - System of Linear Equations
Lecture 14 - Left Invertibility
Lecture 15 - Invertibility of Matrices
Lecture 16 - Triangular Systems
Lecture 17 - LU Decomposition - Part I
Lecture 18 - LU Decomposition - Part II
Lecture 19 - QR Decomposition (Rotators) - Part I
Lecture 20 - QR Decomposition (Rotators) - Part II
Lecture 21 - QR Decomposition (Reflectors) - Part I
Lecture 22 - QR Decomposition (Reflectors) - Part II
Lecture 23 - Matrix Norms
Lecture 24 - Sensitivity Analysis
Lecture 25 - Condition Number of a Matrix
Lecture 26 - Sensitivity Analysis - II
Lecture 27 - Sensitivity Analysis - III
Lecture 28 - Least Squares - Part I
Lecture 29 - Least Squares - Part II
Lecture 30 - Least Squares - Part III
Lecture 31 - Least Squares Data Fitting
Lecture 32 - Examples of LS data fitting
Lecture 33 - Classification using Least Squares
Lecture 34 - Examples of LS classification
Lecture 35 - Constrained Least Squares
Lecture 36 - Multiobjective Least Squares
Lecture 37 - Eigenvalues and Eigenvectors - Part I
Lecture 38 - Eigenvalues and Eigenvectors - Part II
Lecture 39 - Spectral Decomposition Theorem
Lecture 40 - Positive Definite Matrices
Lecture 41 - Singular Value Decomposition (SVD)
Lecture 42 - Proof of SVD
Lecture 43 - Properties of SVD
Lecture 44 - Another Proof of SVD
Lecture 45 - Low Rank Approximations
Lecture 46 - Principal Component Analysis
Lecture 47 - SVD and Pseudo - Inverse
Lecture 48 - SVD and the Least Squares Problem
Lecture 49 - Sensitivity Analysis of the Least Squares Problem
Lecture 50 - Power Method
Lecture 51 - Directed Graphs and Properties
Lecture 52 - Page Ranking Algorithm
Lecture 53 - Inverse Eigen Value Problem
Lecture 54 - Fastest Mixing Markov Chains on Graphs - Part I
Lecture 55 - Fastest Mixing Markov Chains on Graphs - Part II
Lecture 56 - Sparse Solution and Underdetermined Systems
Lecture 57 - Structured Low Rank Approximations - Part I
Lecture 58 - Structured Low Rank Approximations - Part II
Lecture 59 - Structured Low Rank Approximations - Part III
Lecture 60 - Recap