Linear Algebra Done Right, 3rd Edtion Linear Algebra Done Right, 3rd Edtion

Linear Algebra Done Right, 3rd Edtion

3rd Edtion | ISBN: 9783319110790 / 3319110799


expert-verified solutions in this book

Linear Algebra Done Right, 3rd Edtion
Buy on

3rd Edtion | ISBN: 9783319110790 / 3319110799


expert-verified solutions in this book

Buy on

Table of Contents

Chapter 1

Vector Spaces

1.A R^n and C^n Exercises p.11
1.B Definition of Vector Space Exercises p.17
1.C Subspaces Exercises p.24

Chapter 2

Finite-Dimensional Vector Spaces

2.A Span and Linear Independence Exercises p.37
2.B Bases Exercises p.43
2.C Dimension Exercises p.48

Chapter 3

Linear Maps

3.A The Vector Space of Linear Maps Exercises p.57
3.B Null Spaces and Ranges Exercises p.67
3.C Matrices Exercises p.78
3.D Invertibility and Isomorphic Vector Spaces Exercises p.88
3.E Products and Quotients of Vector Spaces Exercises p.98
3.F Duality Exercises p.113

Chapter 4


Exercises p.129

Chapter 5

Eigenvalues, Eigenvectors, And Invariant Subspaces

5.A Invariant Subspaces Exercises p.138
5.B Eigenvectors and Upper-Triangular Matrices Exercises p.153
5.C Eigenspaces and Diagonal Matrices Exercises p.160

Chapter 6

Inner-Product Spaces

6.A Inner Prodcuts and Norms Exercises p.175
6.B Orhtonormal Bases Exercises p.189
6.C Orthogonal Complements and Minimization Problems Exercises p.201

Chapter 7

Operators On Inner-Product Spaces

7.A Self-Adjoint and Normal Operators Exercises p.214
7.B The Spectral Theorem Exercises p.223
7.C Positive Operators and Isometries Exercises p.231
7.D Polar Decomposition and Singular Value Decomposition Exercises p.238

Chapter 8

Operators On Complex Vector Spaces

8.A Generalized Eigenvectors and Nilpotent Operators Exercises p.249
8.B Decomposition of an Operator Exercises p.259
8.C Characteristic and Minimal Polynomials Exercises p.267
8.D Jordan Form Exercises p.274

Chapter 9

Operators On Real Vector Spaces

9.A Complexification Exercises p.285
9.B Operators on Real Inner Product Spaces Exercises p.294

Chapter 10

Trace And Determinant

10.A Trace Exercises p.304
10.B Determinant Exercises p.330
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