Practical Linear Algebra for Data Science

Chapter 1. Introduction

What Is Linear Algebra and Why Learn It?

Linear algebra has an interesting history in mathematics, dating back to the 17th century in the West and much earlier in China. Matrices—the spreadsheets of numbers at the heart of linear algebra—were used to provide a compact notation for storing sets of numbers like geometric coordinates (this was Descartes’s original use of matrices) and systems of equations (pioneered by Gauss). In the 20th century, matrices and vectors were used for multivariate mathematics including calculus, differential equations, physics, and economics.

But most people didn’t need to care about matrices until fairly recently. Here’s the thing: computers are extremely efficient at working with matrices. And so, modern computing gave rise to modern linear algebra. Modern linear algebra is computational, whereas traditional linear algebra is abstract. Modern linear algebra is best learned through code and applications in graphics, statistics, data science, AI, and numerical simulations, whereas traditional linear algebra is learned through proofs and pondering infinite-dimensional vector spaces. Modern linear algebra provides the structural beams that support nearly every algorithm implemented on computers, whereas traditional linear algebra is often intellectual fodder for advanced mathematics university students.

Welcome to modern linear algebra.

Should you learn linear algebra? That depends on whether you want to understand algorithms ...