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Tables of Contents for Linear Algebra
Chapter/Section Title
Page #
Page Count
Vectors, Matrices, and Linear Systems
1
21
Vectors in Euclidean Spaces
1
2
The Norm and the Dot Product
3
2
Matrices and Their Algebra
5
2
Solving Systems of Linear Equations
7
4
Inverses of Square Matrices
11
3
Homogeneous Systems, Subspaces, and Bases
14
3
Application to Population Distribution (Optional)
17
2
Application to Binary Linear Codes (Optional)
19
2
Independence and Linear Transformations of Rn
21
9
Independence and Dimension
21
1
The Rank of a Matrix
22
1
Linear Transformations of Euclidean Spaces
23
2
Linear Transformations of the Plane (Optional)
25
2
Lines and Other Translates (Optional)
27
3
Vector Spaces
30
15
Vector Spaces
30
2
Basic Concepts of Vector Spaces
32
4
Coordinatization of Vectors
36
2
Linear Transformations
38
5
Inner-Product Spaces (Optional)
43
2
Determinants
45
13
Areas, Volumes, and Cross Products
45
3
The Determinant of a Square Matrix
48
2
Computation of Determinants and Cramer's Rule
50
4
Linear Transformations and Determinants (Optional)
54
4
Eigenvalues and Eigenvectors
58
16
Eigenvalues and Eigenvectors
58
7
Diagonalization
65
4
Two Applications
69
5
Orthogonality
74
16
Projections
74
2
The Gram-Schmidt Process
76
3
Orthogonal Matrices
79
4
The Projection Matrix
83
3
The Method of Least Squares
86
4
Change of Basis
90
7
Coordinatization and Change of Basis
90
2
Matrix Representations and Similarity
92
5
Eigenvalues: Further Applications and Computations
97
14
Diagonalization of Quadratic Forms
97
3
Applications to Geometry
100
4
Applications to Extrema
104
4
Computing Eigenvalues and Eigenvectors
108
3
Complex Scalars
111
17
Algebra of Complex Numbers
111
2
Matrices and Vector Spaces with Complex Scalars
113
5
Eigenvalues and Diagonalization
118
4
Jordan Canonical Form
122
6
Solving Large Linear Systems
128
9
Considerations of Time
128
3
The LU-Factorization
131
4
Pivoting, Scaling, and Ill-conditioned Matrices
135
2
Appendix A Mathematical Induction
137