Author(s): Dan Wolczuk
Edition: 1
Publisher: Pearson
Year: 2012
COVER
TITLE PAGE
TABLE OF CONTENTS
A Note to Students -- READ THIS!
ACKNOWLEDGMENTS
1 VECTORS IN EUCLIDEAN SPACE
1.1 Vector Addition and Scalar Multiplication
1.2 Subspaces
1.3 Dot Product
1.4 Projections
2 SYSTEMS OF LINEAR EQUATIONS
2.1 Systems of Linear Equations
2.2 Solving Systems of Linear Equations
3 MATRICES AND LINEAR MAPPINGS
3.1 Operations on Matrices
3.2 Linear Mappings
3.3 Special Subspaces
3.4 Operations on Linear Mappings
4 VECTOR SPACES
4.1 Vector Spaces
4.2 Bases and Dimension
4.3 Coordinates
5 INVERSES AND DETERMINANTS
5.1 Matrix Inverses
5.2 Elementary Matrices
5.3 Determinants
5.4 Determinants and Systems of Equations
5.5 Area and Volume
6 DIAGONALIZATION
6.1 Matrix of a Linear Mapping, Similar Matrices
6.2 Eigenvalues and Eigenvectors
6.3 Diagonalization
6.4 Powers of Matrices
7 FUNDAMENTAL SUBSPACES
7.1 Bases of Fundamental Subspaces
7.2 Subspaces of Linear Mappings
8 LINEAR MAPPINGS
8.1 General Linear Mappings
8.2 Rank-Nullity Theorem
8.3 Matrix of a Linear Mapping
8.4 Isomorphisms
9 INNER PRODUCTS
9.1 Inner Product Spaces
9.2 Orthogonality and Length
9.3 The Gram-Schmidt Procedure
9.4 General Projections
9.5 The Fundamental Theorem
9.6 The Method of Least Squares
10 APPLICATIONS OF ORTHOGONAL MATRICES
10.1 Orthogonal Similarity
10.2 Orthogonal Diagonalization
10.3 Quadratic Forms
10.4 Graphing Quadratic Forms
10.5 Optimizing Quadratic Forms
10.6 Singular Value Decomposition
11 COMPLEX VECTOR SPACES
11.1 Complex Number Review
11.2 Complex Vector Spaces
11.3 Complex Diagonalization
11.4 Complex Inner Products
11.5 Unitary Diagonalization
11.6 Cayley-Hamilton Theorem
