A Crash Course in Applied Linear Algebra

A Crash Course in Applied Linear Algebra

A Crash Course in Applied Linear Algebra. Many people think of Linear Algebra as intimidating, difficult, and great for ending conversations at parties. The truth is that Linear Algebra is extraordinarily useful, often unreasonably so. By studying one equation, y = Ax, you will add an arsenal of tools and intuition to your skillset that can be applied in any technical situation (even nonlinear ones).

Description

Many people think of Linear Algebra as intimidating, difficult, and great for ending conversations at parties. The truth is that Linear Algebra is extraordinarily useful, often unreasonably so. By studying one equation, y = Ax, you will add an arsenal of tools and intuition to your skillset that can be applied in any technical situation (even nonlinear ones).

Abstract

Chances are good that during your education you were required to take a Mathematics course on Linear Algebra, during which you probably covered topics including null spaces, reduced row echelon forms, independence, and a host of similarly abstract concepts. How much of that material do you remember, much less use on a regular basis? Are your eyes glazing over already?

It may amaze you to discover the number of things in your life, from your movie recommendations, to your GPS, to your 401k portfolio, that depend on concepts from Linear Algebra. Linear Algebra provides the theory for many core techniques in Data Science and Statistics, notably linear regression and PCA. You can't even talk about a normal distribution in more than one dimension without introducing matrices!

This talk will cover the highlights of Applied Linear Algebra. We'll discuss the impacts of familiar topics like eigenvalues and rank and introduce some likely unfamiliar topics such as low-rank approximations, quadratic forms, and definiteness. Throughout the talk, I'll bring in geometric interpretations of the math to help create a visual sense for what is happening, as well as application examples from different science and engineering disciplines. Each concept will be demonstrated using Python and Numpy, often in shockingly few lines of code.

My goal is to leave you with an intuition for matrices and linear systems that will unlock your ability to dive into deeper subjects as you continue in your own growth and exploration.

Prerequisites: a basic knowledge of vectors, matrices, and matrix multiplication

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