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October 6, 2021

What would we do without Linear Algebra, Part 3: Singular Value Decomposition & Principal Component

About This Video

In this third workshop in linear algebra, we will investigate the link between Principal Component Analysis and the Singular Value Decomposition. Along the way, we are introduced to several linear algebra concepts including linear regression, eigenvalues and eigenvectors and conditioning of a system. We will use shared python scripts and several examples to demonstrate the ideas discussed.

This workshop builds on the previous 2 workshops in linear algebra (Part I and Part II), and we will assume that the linear algebra concepts introduced in those workshops are familiar to the audience. They include: vector algebra (including inner products, angle between vectors), matrix-vector multiplications, matrix-matrix multiplications, matrix-vectors solves, singularity, and singular values.

1. Code is available for viewers to follow along:…
2. The covariance matrix is defined for centered X, and the inequality n 1 given is strict.

This workshop was conducted by Laura Lyman, phD student at Stanford University, ICME.

In This Video
Instructor of Mathematics, Statistics, and Computer Science (MSCS), Macalester College​

Laura Lyman is an instructor of mathematics, statistics, and computer science at Macalester College, a top-tier liberal arts school located in Saint Paul, Minnesota. She is an applied mathematician who researches how uncertainty propagates through models in science and engineering using a class of tools called spectral methods.

Prior to her current role, Laura did her PhD work at Stanford University in the Institute for Computational and Mathematical Engineering (ICME). She is a recipient of the Stanford Centennial Teaching Award and the ICME Instructor Award for 2021-2022.