Vector Spaces and Subspaces · Advanced Linear Algebra

Introduction

What this guide covers

Introduction Rigorous Linear Algebra Module

Overview

Topics covered

• Introduction
• Vector Spaces and Subspaces: Structure, Dimension and Topology
• Historical and geometric evolution
• The formal axiomatic definition
• 2.1 Axioms of vector addition
• 2.2 Axioms of multiplication by a scalar

Related concepts

Main connections

• Linear algebra & matrices
• Conditional probability & independence
• Principal component analysis (PCA)
• Calculus & differentiation
• Supervised machine learning
• Causal inference & potential outcomes

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.