Interactive

Definition of a Vector Space

This is an interactive companion to Section 1B of Sheldon Axler's Linear Algebra Done Right (4th ed.). It maps the section's definitions, results, examples, and notations, and shows how they are related. For more information, click any box in the diagram or the help button.

Material from Axler, Linear Algebra Done Right (4th ed.) · CC BY-NC 4.0

How to read this map

Section 1B of Axler’s Linear Algebra Done Right (4th ed.) states the definition of a vector space and covers basic examples and results. Each named statement in the section has a box here, numbered exactly as in Axler.

There are two ways to view the diagram, chosen with the Layout buttons. Page order places each statement on the page where it appears in Axler, so you can follow along with the book. Conceptual puts the most important statement, 1.20, at the center and arranges the rest radially around it.

Statement boxes are colored by kind: definition, result, notation, example.
Click a box to read the precise statement. Click an arrow to see how one statement leads to another.

Definitions, examples, statements, and proofs are quoted from Axler, Linear Algebra Done Right, 4th ed., used under CC BY-NC 4.0. Some quoted material has been adapted for this format.