What is included with this book?
Vectors | p. 1 |
The Geometry and Algebra of Vectors | p. 3 |
Length and Angle: The Dot Product | p. 11 |
Exploration: Vectors and Geometry | p. 25 |
Lines and Planes | p. 27 |
Exploration: The Cross Product | p. 45 |
Code Vectors and Modular Arithmetic | p. 47 |
Chapter 1 Review | p. 53 |
Systems of Linear Equations | p. 61 |
Introduction to Systems of Linear Equations | p. 63 |
Exploration: Lies My Computer Told Me | p. 69 |
Direct Methods for Solving Linear Systems | p. 71 |
Exploration: Partial Pivoting | p. 87 |
Exploration: An Introduction to the Analysis of Algorithms | p. 89 |
Spanning Sets and Linear Independence | p. 91 |
Applications | p. 109 |
Iterative Methods for Solving Linear Systems | p. 121 |
Chapter 2 Review | p. 127 |
Matrices | p. 135 |
Matrix Operations | p. 137 |
Matrix Algebra | p. 143 |
The Inverse of a Matrix | p. 155 |
The LU Factorization | p. 163 |
Subspaces, Basis, Dimension, and Rank | p. 177 |
Introduction to Linear Transformations | p. 195 |
Applications | p. 209 |
Chapter 3 Review | p. 221 |
Eigenvalues and Eigenvectors | p. 231 |
Introduction to Eigenvalues and Eigenvectors | p. 233 |
Determinants | p. 247 |
Exploration: Geometric Applications of Determinants | p. 269 |
Eigenvalues and Eigenvectors of n x n Matrices | p. 275 |
Similarity and Diagonalization | p. 287 |
Iterative Methods for Computing Eigenvalues | p. 299 |
Applications and the Perron-Frobenius Theorem | p. 313 |
Chapter 4 Review | p. 327 |
Orthogonality | p. 337 |
Orthogonality in Rn | p. 339 |
Orthogonal Complements and Projections | p. 349 |
The Gram-Schmidt Process and the QR Factorization | p. 355 |
Exploration: The Modified QR Factorization | p. 359 |
Exploration: Approximating Eigenvalues with the QR Algorithm | p. 361 |
Orthogonal Diagonalization of Symmetric Matrices | p. 363 |
Applications | p. 369 |
Chapter 5 Review | p. 381 |
Vector Spaces | p. 395 |
Vector Spaces and Subspaces | p. 397 |
Linear Independence, Basis, and Dimension | p. 403 |
Exploration: Magic Squares | p. 413 |
Change of Basis | p. 415 |
Linear Transformations | p. 423 |
The Kernel and Range of a Linear Transformation | p. 429 |
The Matrix of a Linear Transformation | p. 439 |
Exploration: Tilings, Lattices, and Crystallographic Restriction | p. 449 |
Applications | p. 451 |
Chapter 6 Review | p. 457 |
Distance and Approximation | p. 471 |
Inner Product Spaces | p. 473 |
Exploration: Vectors and Matrices with Complex Entries | p. 481 |
Exploration: Geometric Inequalities and Optimization Problems | p. 485 |
Norms and Distance Functions | p. 489 |
Least Squares Approximation | p. 497 |
The Singular Value Decomposition | p. 505 |
Applications | p. 515 |
Chapter 7 Review | p. 521 |
Key Definitions and Concepts | p. 535 |
Theorems | p. 559 |
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