Algorithm Design Using Linear Algebra

Module 1 - Review of Linear Algebra [Notes]
References - [Str] Introduction to Linear Algebra by Gilbert Strang, 5th edition.
[Rao] - Advanced Matrix Theory and Linear Algebra for Engineers, R. Vittal Rao.

Module 2 - Graphs through the lens of Linear Algebra: Graph Properties via Eigenvalues, Graph Drawing using Eigenvectors. [Notes]
References - [Spi] Spectral and Algebraic Graph Theory by Dan Spielman
[Lau22] - Eigenvalues and Polynomials, Lap Chi Lau

Module 3 - Graph Partitioning: Spectral Clustering Algorithm, Expanders aka Magical Graphs. [Notes]
References - [Spi] Spectral and Algebraic Graph Theory by Dan Spielman
[Lau22] - Eigenvalues and Polynomials, Lap Chi Lau

Module 4 - Random Walks: Basic Setup, Applications- a) Google's Page Rank Algorithm, and b) Random Sampling in Social Networks. [Notes]
References - [Spi] Spectral and Algebraic Graph Theory by Dan Spielman
[Lau22] - Eigenvalues and Polynomials, Lap Chi Lau