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Tables of Contents for Linear Algebra Done Right
Chapter/Section Title
Page #
Page Count
Preface to the Instructor
ix
4
Preface to the Student
xiii
2
Acknowledgments
xv
 
CHAPTER 1 Vector Spaces
1
20
Complex Numbers
2
2
Definition of Vector Space
4
7
Properties of Vector Spaces
11
2
Subspaces
13
1
Sums and Direct Sums
14
5
Exercises
19
2
CHAPTER 2 Finite-Dimensional Vector Spaces
21
16
Span and Linear Independence
22
5
Bases
27
4
Dimension
31
4
Exercises
35
2
CHAPTER 3 Linear Maps
37
26
Definitions and Examples
38
3
Null Spaces and Ranges
41
7
The Matrix of a Linear Map
48
5
Invertibility
53
6
Exercises
59
4
CHAPTER 4 Polynomials
63
12
Degree
64
3
Complex Coefficients
67
2
Real Coefficients
69
4
Exercises
73
2
CHAPTER 5 Eigenvalues and Eigenvectors
75
22
Invariant Subspaces
76
4
Polynomials Applied to Operators
80
1
Upper-Triangular Matrices
81
6
Diagonal Matrices
87
4
Invariant Subspaces on Real Vector Spaces
91
3
Exercises
94
3
CHAPTER 6 Inner-Product Spaces
97
30
Inner Products
98
4
Norms
102
4
Orthonormal Bases
106
5
Orthogonal Projections and Minimization Problems
111
6
Linear Functionals and Adjoints
117
5
Exercises
122
5
CHAPTER 7 Operators on Inner-Product Spaces
127
36
Self-Adjoint and Normal Operators
128
4
The Spectral Theorem
132
6
Normal Operators on Real Inner-Product Spaces
138
6
Positive Operators
144
3
Isometries
147
5
Polar and Singular-Value Decompositions
152
6
Exercises
158
5
CHAPTER 8 Operators on Complex Vector Spaces
163
30
Generalized Eigenvectors
164
4
The Characteristic Polynomial
168
5
Decomposition of an Operator
173
4
Square Roots
177
2
The Minimal Polynomial
179
4
Jordan Form
183
5
Exercises
188
5
CHAPTER 9 Operators on Real Vector Spaces
193
20
Eigenvalues of Square Matrices
194
1
Block Upper-Triangular Matrices
195
3
The Characteristic Polynomial
198
12
Exercises
210
3
CHAPTER 10 Trace and Determinant
213
34
Change of Basis
214
2
Trace
216
6
Determinant of an Operator
222
3
Determinant of a Matrix
225
11
Volume
236
8
Exercises
244
3
Symbol Index
247
2
Index
249