Linear Algebra - A Modern Introduction (4e) ISM

Front Cover
Table of Contents
1 - Vectors - pg. 3
	1.1 - The Geometry and Algebra of Vectors - pg. 3
	1.2 - Length and Angle: The Dot Product - pg. 10
		Exploration: Vectors and Geometry - pg. 25
	1.3 - Lines and Planes - pg. 27
		Exploration: The Cross Product - pg. 41
	1.4 - Applications - pg. 44
		Chapter Review - pg. 48
2 - Systems of Linear Equations - pg. 53
	2.1 - Introduction to Systems of Linear Equations - pg. 53
	2.2 - Direct Methods for Solving Linear Systems - pg. 58
		Exploration: Lies My Computer Told Me - pg. 75
		Exploration: Partial Pivoting - pg. 75
		Exploration: An Introduction to the Analysis of Algorithms - pg. 77
	2.3 - Spanning Sets and Linear Independence - pg. 79
	2.4 - Applications - pg. 93
	2.5 - Iterative Methods for Solving Linear Systems - pg. 112
		Chapter Review - pg. 123
3 - Matrices - pg. 129
	3.1 - Matrix Operations - pg. 129
	3.2 - Matrix Algebra - pg. 138
	3.3 - The Inverse of a Matrix - pg. 150
	3.4 - The LU Factorization - pg. 164
	3.5 - Subspaces, Basis, Dimension, and Rank - pg. 176
	3.6 - Introduction to Linear Transformations - pg. 192
	3.7 - Applications - pg. 209
		Chapter Review - pg. 230
4 - Eigenvalues and Eigenvectors - pg. 235
	4.1 - Introduction to Eigenvalues and Eigenvectors - pg. 235
	4.2 - Determinants - pg. 250
		Exploration: Geometric Applications of Determinants - pg. 263
	4.3 - Eigenvalues and Eigenvectors of n × n Matrices - pg. 270
	4.4 - Similarity and Diagonalization - pg. 291
	4.5 - Iterative Methods for Computing Eigenvalues - pg. 308
	4.6 - Applications and the Perron-Frobenius Theorem - pg. 326
		Chapter Review - pg. 365
5 - Orthogonality - pg. 371
	5.1 - Orthogonality in Rn - pg. 371
	5.2 - Orthogonal Complements and Orthogonal Projections - pg. 379
	5.3 - The Gram-Schmidt Process and the QR Factorization - pg. 388
		Exploration: The Modified QR Process - pg. 398
		Exploration: Approximating Eigenvalues with the QR Algorithm - pg. 402
	5.4 - Orthogonal Diagonalization of Symmetric Matrices - pg. 405
	5.5 - Applications - pg. 417
		Chapter Review - pg. 442
6 - Vector Spaces - pg. 451
	6.1 - Vector Spaces and Subspaces - pg. 451
	6.2 - Linear Independence, Basis, and Dimension - pg. 463
		Exploration: Magic Squares - pg. 477
	6.3 - Change of Basis - pg. 480
	6.4 - Linear Transformations - pg. 491
	6.5 - The Kernel and Range of a Linear Transformation - pg. 498
	6.6 - The Matrix of a Linear Transformation - pg. 507
		Exploration: Tiles, Lattices, and the Crystallographic Restriction - pg. 525
	6.7 - Applications - pg. 527
		Chapter Review - pg. 531
7 - Distance and Approximation - pg. 537
	7.1 - Inner Product Spaces - pg. 537
		Exploration: Vectors and Matrices with Complex Entries - pg. 546
		Exploration: Geometric Inequalities and Optimization Problems - pg. 553
	7.2 - Norms and Distance Functions - pg. 556
	7.3 - Least Squares Approximation - pg. 568
	7.4 - The Singular Value Decomposition - pg. 590
	7.5 - Applications - pg. 614
		Chapter Review - pg. 625
8 - Codes - pg. 633
	8.1 - Code Vectors - pg. 633
	8.2 - Error-Correcting Codes - pg. 637
	8.3 - Dual Codes - pg. 641
	8.4 - Linear Codes - pg. 647
	8.5 - The Minimum Distance of a Code - pg. 650