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Course11110516560 lectures

Applied Linear Algebra in AI and ML

Prof. Swanand Khare · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 01 : Vector Spaces Video
  2. Lecture 02 : Vector Subspaces Video
  3. Lecture 03 : Linear Span and Linear Dependence Video
  4. Lecture 04 : Linear Independence Video
  5. Lecture 05 : Basis and Dimension Video

week-02

  1. Lecture 06 : Linear Functionals Video
  2. Lecture 07 : Norm of Vector Part - I Video
  3. Lecture 08 : Norm of Vector Part - II Video
  4. Lecture 09 : Linear Functions Video
  5. Lecture 10 : Affine Functions and Examples Video

week-03

  1. Lecture 11: Examples of Linear and Affine Functions Video
  2. Lecture 12: Function Composition Video
  3. Lecture 13: System of Linear Equations Video
  4. Lecture 14: Left Invertibility Video
  5. Lecture 15: Invertibility of Matrices Video

week-04

  1. Lecture 16: Triangular Systems Video
  2. Lecture 17: LU Decomposition Part - I Video
  3. Lecture 18: LU Decomposition Part - II Video
  4. Lecture 19: QR Decomposition (Rotators - Part I) Video
  5. Lecture 20: QR Decomposition (Rotators - Part II) Video

week-05

  1. Lecture 21: QR Decomposition (Reflectors - Part I) Video
  2. Lecture 22: QR Decomposition (Reflectors - Part II) Video
  3. Lecture 23: Matrix Norms Video
  4. Lecture 24: Sensitivity Analysis Video
  5. Lecture 25: Condition Number of a Matrix Video

week-06

  1. Lecture 26: Sensitivity Analysis -II Video
  2. Lecture 28: Least Squares - Part I Video
  3. Lecture 29: Least Squares - Part II Video
  4. Lecture 30: Least Squares - Part III Video

week-07

  1. Lecture 31: Least Squares Data Fitting Video
  2. Lecture 32: Examples of LS data fitting Video
  3. Lecture 33: Classification using Least Squares Video
  4. Lecture 34: Examples of LS classification Video
  5. Lecture 35: Constrained Least Squares Video

week-08

  1. Lecture 36: Multiobjective Least Squares Video
  2. Lecture 37: Eigenvalues and Eigenvectors (Part - I) Video
  3. Lecture 38: Eigenvalues and Eigenvectors (Part - II) Video
  4. Lecture 39: Spectral Decomposition Theorem Video
  5. Lecture 40: Positive Definite Matrices Video

week-09

  1. Lecture 27: Sensitivity Analysis -III Video
  2. Lecture 41 : Singular Value Decomposition (SVD) Video
  3. Lecture 42 : Proof of SVD Video
  4. Lecture 43 : Properties of SVD Video
  5. Lecture 44 : Another Proof of SVD Video
  6. Lecture 45 : Low Rank Approximations Video

week-10

  1. Lecture 46 : Principal Component Analysis Video
  2. Lecture 47 : SVD and Pseudo - Inverse Video
  3. Lecture 48 : SVD and the Least Squares Problem Video
  4. Lecture 49 : Sensitivity Analysis of the Least Squares Problem Video
  5. Lecture 50 : Power Method Video

week-11

  1. Lecture 51 : Directed Graphs and Properties Video
  2. Lecture 52 : Page Ranking Algorithm Video
  3. Lecture 53 : Inverse Eigen Value Problem Video
  4. Lecture 54 : Fastest Mixing Markov Chains on Graphs (Part I) Video
  5. Lecture 55 : Fastest Mixing Markov Chains on Graphs (Part II) Video

week-12

  1. Lecture 56: Sparse Solution and Underdetermined Systems Video
  2. Lecture 57: Structured Low Rank Approximations (Part I) Video
  3. Lecture 58: Structured Low Rank Approximations (Part II) Video
  4. Lecture 59: Structured Low Rank Approximations (Part III) Video
  5. Lecture 60: Recap Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. Swanand Khare
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.
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