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A rough guide to linear algebra

Contents

A rough guide to linear algebra

Preface

1 Sets

Chapter overview
1.1 Sets and maps
1.2 Products, coproducts, and sets of maps
1.3 Fun with diagrams
1.4 Equivalence classes

2 Vector spaces

Chapter overview
2.1 Fields
2.2 Vector spaces
2.3 Matrices
2.4 Products and direct sums
2.5 Subspaces and quotients
2.6 Vector spaces from linear maps
2.7 Bases and dimension
2.8 Dual spaces
2.9 Linear algebra in combinatorics

3 Multilinear algebra

Chapter overview
3.1 Bilinear maps and tensor products
3.2 Symmetric and exterior algebras
3.3 The determinant
3.4 Computing the inverse matrix

4 Linear algebra without division

Chapter overview
4.1 Commutative rings
4.2 Modules
4.3 Classification of finitely generated modules over a PID
4.4 Frobenius and Jordan normal form
4.5 Eigenvalues and eigenvectors

5 Linear algebra over R and C

Chapter overview
5.1 A bit of analysis
5.2 Inner products
5.3 Operators on Hilbert spaces
5.4 The spectral theorem
5.5 Positivity of operators

Epilogue
Subject index
Search

A rough guide to linear algebra

Preface

1 Sets

Chapter overview
1.1 Sets and maps
1.2 Products, coproducts, and sets of maps
1.3 Fun with diagrams
1.4 Equivalence classes

2 Vector spaces

Chapter overview
2.1 Fields
2.2 Vector spaces
2.3 Matrices
2.4 Products and direct sums
2.5 Subspaces and quotients
2.6 Vector spaces from linear maps
2.7 Bases and dimension
2.8 Dual spaces
2.9 Linear algebra in combinatorics

3 Multilinear algebra

Chapter overview
3.1 Bilinear maps and tensor products
3.2 Symmetric and exterior algebras
3.3 The determinant
3.4 Computing the inverse matrix

4 Linear algebra without division

Chapter overview
4.1 Commutative rings
4.2 Modules
4.3 Classification of finitely generated modules over a PID
4.4 Frobenius and Jordan normal form
4.5 Eigenvalues and eigenvectors

5 Linear algebra over R and C

Chapter overview
5.1 A bit of analysis
5.2 Inner products
5.3 Operators on Hilbert spaces
5.4 The spectral theorem
5.5 Positivity of operators

Epilogue
Subject index
Search

Reference

Search

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© Dongryul Kim Web edition: August 25, 2026 CC BY 4.0 Latest PDF GitHub repository