دانلود کتاب Linear Algebra: A Modern Introduction

فهرست مطالب :

Front Cover
Table of Contents
Preface
To the Instructor
To the student
Chapter 1 - Vectors - pg. 1
1.0 - Introduction: The Racetrack Game - pg. 1
1.1 - The Geometry and Algebra of Vectors - pg. 3
1.2 - Length and Angle: The Dot Product - pg. 18
Exploration: Vectors and Geometry - pg. 32
1.3 - Lines and Planes - pg. 34
Exploration: The Cross Product - pg. 48
Writing Project: The Origins of the Dot Product and Cross Product - pg. 49
1.4 - Applications - pg. 50
Force Vectors - pg. 50
Chapter Review - pg. 55
Chapter 2 - Systems of Linear Equations - pg. 57
2.0 - Introduction: Triviality - pg. 57
2.1 - Introduction to Systems of Linear Equations - pg. 58
2.2 - Direct Methods for Solving Linear Systems - pg. 64
Writing Project: A History of Gaussian Elimination - pg. 82
Explorations: Lies My Computer Told Me - pg. 83
Partial Pivoting - pg. 84
Counting Operations: An Introduction to the Analysis of Algorithms - pg. 85
2.3 - Spanning Sets and Linear Independence - pg. 88
2.4 - Applications - pg. 99
Allocation of Resources - pg. 99
Balancing Chemical Equations - pg. 101
Network Analysis - pg. 102
Electrical Networks - pg. 104
Linear Economic Models - pg. 107
Finite Linear Games - pg. 109
Vignette: The Global Positioning System - pg. 121
2.5 - Iterative Methods for Solving Linear Systems - pg. 124
Chapter Review - pg. 134
Chapter 3 - Matrices - pg. 136
3 - Introduction: Matrices in Action - pg. 136
3.1 - Matrix Operations - pg. 138
3.2 - Matrix Algebra - pg. 154
3.3 - The Inverse of a Matrix - pg. 163
3.4 - The LU Factorization - pg. 180
3.5 - Subspaces, Basis, Dimension, and Rank - pg. 191
3.6 - Introduction to Linear Transformations - pg. 211
Vignette: Robotics - pg. 226
3.7 - Applications - pg. 230
Markov Chains - pg. 230
Linear Economic Models - pg. 235
Population Growth - pg. 239
Graphs and Digraphs - pg. 241
Chapter Review - pg. 251
Chapter 4 - Eigenvalues and Eigenvectors - pg. 253
4 - Introduction: A Dynamical System on Graphs - pg. 253
4.1 - Introduction to Eigenvalues and Eigenvectors - pg. 254
4.2 - Determinants - pg. 263
Writing Project: Which Came First: The Matrix or the Determinant? - pg. 283
Vignette: Lewis Carroll\'s Condensation Method - pg. 284
Exploration: Geometric Applications of Determinants - pg. 286
4.3 - Eigenvalues and Eigenvectors of n X n Matrices - pg. 292
4.4 - Similarity and Diagonalization - pg. 301
4.5 - Iterative Methods for Computing Eigenvalues - pg. 311
4.6 - Applications and the Perron-Frobenius Theorem - pg. 325
Markov Chains - pg. 325
Population Growth - pg. 330
The Perron-Frobenius Theorem - pg. 332
Linear Recurrence Relations - pg. 335
Systems of Linear Differential Equations - pg. 340
Discrete Linear Dynamical Systems - pg. 348
Vignette: Ranking Sports Teams and Searching the Internet - pg. 356
Chapter Review - pg. 364
Chapter 5 - Orthogonality - pg. 366
5.0 - Introduction: Shadows on a Wall - pg. 366
5.1 - Orthogonality in IR\" - pg. 368
5.2 - Orthogonal Complements and Orthogonal Projections - pg. 378
5.3 - The Gram-Schmidt Process and the QR Factorization - pg. 388
Explorations: The Modified QR Factorization - pg. 396
Approximating Eigenvalues with the QR Algorithm - pg. 398
5.4 - Orthogonal Diagonalization of Symmetric Matrices - pg. 400
5.5 - Applications - pg. 408
Quadratic Forms - pg. 408
Graphing Quadratic Equations - pg. 415
Chapter Review - pg. 425
Chapter 6 - Vector Spaces - pg. 427
6 - Introduction: Fibonacci in (Vector) Space - pg. 427
6.1 - Vector Spaces and Subspaces - pg. 429
Writing Project: The Rise of Vector Spaces - pg. 443
6.2 - Linear Independence, Basis, and Dimension - pg. 443
Exploration: Magic Squares - pg. 460
6.3 - Change of Basis - pg. 463
6.4 - Linear Transformations - pg. 472
6.5 - The Kernel and Range of a Linear Transformation - pg. 481
6.6 - The Matrix of a Linear Transformation - pg. 497
Exploration: Tilings, Lattices, and the Crystallographic Restriction - pg. 515
6.7 - Applications - pg. 518
Homogeneous Linear Differential Equations - pg. 518
Chapter Review - pg. 527
Chapter 7 - Distance and Approximation - pg. 529
7.0 - Introduction: Taxicab Geometry - pg. 529
7.1 - Inner Product Spaces - pg. 531
Explorations: Vectors and Matrices with Complex Entries - pg. 543
Geometric Inequalities and Optimization Problems - pg. 547
7.2 - Norms and Distance Functions - pg. 552
7.3 - Least Squares Approximation - pg. 568
7.4 - The Singular Value Decomposition - pg. 590
Vignette: Digital Image Compression - pg. 607
7.5 - Applications - pg. 610
Approximation of Functions - pg. 610
Chapter Review - pg. 618
Chapter 8 - Codes Online only - pg. 620
8.1 - Code Vectors - pg. 620
Vignette: The Codabar System - pg. 626
8.2 - Error-Correcting Codes - pg. 627
8.3 - Dual Codes - pg. 632
8.4 - Linear Codes - pg. 639
8.5 - The Minimum Distance of a Code - pg. 644