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Elementary Linear Algebra : Applications Version by Howard Anton and Chris Rorres (2013, Ringbound)

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By Anton, Howard, Rorres, Chris.

About this product

Product Identifiers

PublisherWiley & Sons, Incorporated, John

ISBN-101118474228

ISBN-139781118474228

eBay Product ID (ePID)172890928

Product Key Features

Number of Pages800 Pages

Publication NameElementary Linear Algebra : Applications Version

LanguageEnglish

SubjectAlgebra / Linear

Publication Year2013

TypeTextbook

Subject AreaMathematics

AuthorHoward Anton, Chris Rorres

FormatRingbound

Dimensions

Item Height0.9 in

Item Weight44.1 Oz

Item Length9.9 in

Item Width8 in

Additional Product Features

Edition Number11

Intended AudienceCollege Audience

Dewey Edition22

Dewey Decimal512/.5

Table Of ContentCHAPTER 1 Systems of Linear Equations and Matrices 1 1.1 Introduction to Systems of Linear Equations 2 1.2 Gaussian Elimination 11 1.3 Matrices and Matrix Operations 25 1.4 Inverses; Algebraic Properties of Matrices 39 1.5 Elementary Matrices and a Method for Finding A-1 52 1.6 More on Linear Systems and Invertible Matrices 61 1.7 Diagonal, Triangular, and Symmetric Matrices 67 1.8 Matrix Transformations 75 1.9 Applications of Linear Systems 84 Network Analysis (Traffic Flow) 84 Electrical Circuits 86 Balancing Chemical Equations 88 Polynomial Interpolation 91 1.10 Application:Leontief Input-Output Models 96 CHAPTER 2 Determinants 105 2.1 Determinants by Cofactor Expansion 105 2.2 Evaluating Determinants by Row Reduction 113 2.3 Properties of Determinants; Cramer''s Rule 118 CHAPTER 3 Euclidean Vector Spaces 131 3.1 Vectors in 2-Space, 3-Space, and n -Space 131 3.2 Norm, Dot Product, and Distance in Rn 142 3.3 Orthogonality 155 3.4The Geometry of Linear Systems 164 3.5 Cross Product 172 CHAPTER 4 General Vector Spaces 83 4.1 Real Vector Spaces 183 4.2 Subspaces 191 4.3 Linear Independence 202 4.4 Coordinates and Basis 212 4.5 Dimension 221 4.6 Change of Basis 229 4.7 Row Space, Column Space, and Null Space 237 4.8 Rank, Nullity, and the Fundamental Matrix Spaces 248 4.9 Basic Matrix Transformations in R2 and R3 259 4.10 Properties of Matrix Transformations 270 4.11Application: Geometry of Matrix Operators on R2 280 CHAPTER 5 Eigenvalues and Eigenvectors 291 5.1 Eigenvalues and Eigenvectors 291 5.2 Diagonalization 302 5.3 Complex Vector Spaces 313 5.4 Application: Differential Equations 326 5.5 Application: Dynamical Systems and Markov Chains 332 CHAPTER 6 Inner Product Spaces 345 6.1 Inner Products 345 6.2 Angle and Orthogonality in Inner Product Spaces 355 6.3 Gram-Schmidt Process; QR -Decomposition 364 6.4 Best Approximation; Least Squares 378 6.5 Application: Mathematical Modeling Using Least Squares 387 6.6 Application: Function Approximation; Fourier Series 394 CHAPTER 7 Diagonalization and Quadratic Forms 401 7.1 Orthogonal Matrices 401 7.2 Orthogonal Diagonalization 409 7.3 Quadratic Forms 417 7.4 Optimization Using Quadratic Forms 429 7.5 Hermitian, Unitary, and Normal Matrices 437 CHAPTER 8 General Linear Transformations 447 8.1 General Linear Transformations 447 8.2 Compositions and Inverse Transformations 458 8.3 Isomorphism 466 8.4 Matrices for General Linear Transformations 472 8.5 Similarity 481 CHAPTER 9 Numerical Methods 491 9.1 LU -Decompositions 491 9.2 The Power Method 501 9.3 Comparison of Procedures for Solving Linear Systems 509 9.4 Singular Value Decomposition 514 9.5 Application: Data Compression Using Singular Value Decomposition 521 CHAPTER 10 Applications of Linear Algebra 527 10.1 Constructing Curves and Surfaces Through Specified Points 528 10.2 The Earliest Applications of Linear Algebra 533 10.3 Cubic Spline Interpolation 540 10.4 Markov Chains 551 10.5 Graph Theory 561 10.6 Games of Strategy 570 10.7 Leontief Economic Models 579 10.8 Forest Management 588 10.9 Computer Graphics 595 10.10 Equilibrium Temperature Distributions 603 10.11 Computed Tomography 613 10.12 Fractals 624 10.13 Chaos 639 10.14 Cryptography 652 10.15 Genetics 663 10.16 Age-Specific Population Growth 673 10.17 Harvesting of Animal Populations 683 10.18 A Least Squares Model for Human Hearing 691 10.19 Warps and Morphs 697 10.20 Internet Search Engines 706 APPENDIX A Working with Proofs A1 APPENDIX B Complex Numbers A5 Answers to exercises A13 Index I1

SynopsisThis text is an unbound, binder-ready edition. Elementary Linear Algebra 11th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. The 11th edition helps readers perceive linear algebra as a cohesive subject rather than a collection of definitions and techniques by including proof sketches and visual aids for visual learners., Elementary Linear Algebra: Applications Version, 11th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.