Preface

Linear algebra studies objects that can be added and scaled, together with the maps that respect those two operations. It is the shared language of geometry, calculus, probability, statistics and machine learning.

How to read this book#

Every chapter unfolds in the same order: a picture, then a definition, then examples. Feel free to skip proofs on a first reading, but do not skip the examples.

Draw it first

When you meet a new definition, draw it in the plane . Most statements that make sense in two dimensions generalize to by notation alone.

Notation#

Vectors are written as columns¹, for example

How this book relates to the rest of the series#

The rigorous definition of a limit lives in Limits of Calculus. Linearity of expectation (see Random Variables › Linearity of expectation) says, at heart, that expectation is a linear map.

When you are ready, start with Vectors.