NOC:Applied Linear Algebra in AI and ML

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