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Tables of Contents for Linear Algebra
Chapter/Section Title
Page #
Page Count
Preface
xi
To the Student
xvii
Suggested Lecture Schedule
xix
The Geometry of the Plane and 3-Space
1
68
Vectors
1
15
Length and Direction
16
10
Lines, Planes, and the Cross Product of Vectors
26
19
Projections
45
9
Euclidean n-Space
54
15
Review Exercises
66
3
Matrices and Linear Equations
69
98
The Algebra of Matrices
69
19
The Inverse and Transpose of a Matrix
88
10
Systems of Linear Equations
98
19
Homogeneous Systems and Linear Independence
117
8
The LU Factorization of a Matrix
125
19
LDU Factorizations
144
8
Finding the Inverse of a Matrix
152
15
Review Exercises
163
4
Determinants, Eigenvalues, Eigenvectors
167
50
The Determinant of a Matrix
167
10
Properties of Determinants
177
16
The Eigenvalues and Eigenvectors of a Matrix
193
10
Similarity and Diagonalization
203
14
Review Exercises
214
3
Vector Spaces
217
68
The Theory of Linear Equations
217
16
Basic Terminology and Concepts
233
20
Basis and Dimension; Rank and Nullity
253
21
One-Sided Inverses
274
11
Review Exercises
282
3
Linear Transformations
285
50
Linear Transformations of Rn
285
16
Matrix Multiplication Revisited
301
7
The Matrices of a Linear Transformation
308
13
Changing Coordinates
321
14
Review Exercises
331
4
Orthogonality
335
66
Projection Matrices and Least Squares Approximation
335
18
The Gram-Schmidt Algorithm and QR Factorization
353
18
Orthogonal Subspaces and Complements
371
16
The Pseudoinverse of a Matrix
387
14
Review Exercises
398
3
The Spectral Theorem
401
56
Complex Numbers and Vectors
401
14
Complex Matrices
415
8
Unitary Diagonalization
423
18
Real Symmetric Matrices
441
7
The Singular Value Decomposition
448
9
Review Exercises
455
2
Applications
457
Data Fitting
457
5
Linear Recurrence Relations
462
6
Markov Processes
468
6
Quadratic Forms and Conic Sections
474
5
Graphs
479
Appendix: Show and Prove
1
1
Solutions to True/False Questions and Selected Exercises
1
1
Glossary
1
1
Index
1