Verfügbarkeit: Linear algebra with applications

Linear algebra with applications:

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Bibliographische Detailangaben
1. Verfasser:	Williams, Gareth (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boston [u.a.] Jones and Bartlett 2008
Ausgabe:	6. ed.
Schlagworte:	Algebras, Linear > Textbooks Lineare Algebra
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XVI, 544 S.t. graph. Darst.
ISBN:	9780763746315 0763746312

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface xi Part 1 Linear Equations, Vectors, and Matrices 1__________ f Linear Equations and Vectors 3 ED Matrices and Systems of Linear Equations 3 [Q Gauss-Jordan Elimination 15 The Vector Space R 24 Basis and Dimension 33 Dot Product, Norm, Angle, and Distance 38 (Option: This section can be covered just before Section 4.6.) Curve Fitting, Electrical Networks, and Traffic Flow 49 Chapter 1 Review Exercises 57 2 Matrices and Linear Transformations 61 Addition, Scalar Multiplication, and Multiplication of Matrices 61 Properties of Matrix Operations 74 Symmetric Matrices and Sedation in Archaeology 85 The Inverse of a Matrix and Cryptography 95 Matrix Transformations, Rotations, and Dilations 108 Linear Transformations, Graphics, and Fractals 119 The Leontief Input-Output Model in Economics 129 Sections marked with an asterisk are optional. The instructor can use these sections to build around the core material to give the course the desired flavor. vi Contents РП Markov Chains, Population Movements, and Genetics 135 И! A Communication Model and Group Relationships in Sociology 141 Chapter 2 Review Exercises 151 3 Determinants and Eigenvectors 155 Introduction to Determinants 155 Properties of Determinants 163 Determinants, Matrix Inverses, and Systems of Linear Equations 172 Eigenvalues and Eigenvectors 180 ff^ Google, Demography, and Weather Prediction (Option: Section 5.3, Diagonalization of Matrices, can be covered here.) 187 Chapter 3 Review Exercises 194 Part 2 Vector Spaces 197_____________________________ General Vector Spaces 199 ЕЖ1 General Veđor Spaces and Subspaces 199 СИ Linear Combinations 208 Linear Dependence and Independence 215 Properties of Bases 220 Rank 228 Orthonormal Vectors and Projections 237 Kernel, Range, and the Rank/Nullity Theorem 249 One-to-One Transformations and Inverse Transformations 259 Transformations and Systems of Linear Equations 264 Chapter 4 Review Exercises 271 5 Coordinate Representations 275 Coordinate Vectors 275 Matrix Representations of Linear Transformations 283 Diagonalization of Matrices 292 Contents vii Quadratic Forms, Difference Equations, and Normal Modes 303 Chapter 5 Review Exercises 314 jjj Inner Product Spaces 317 Inner Product Spaces 317 Non-Euclidean Geometry and Special Relativity 326 Approximation of Fundions and Coding Theory 331 Least Squares Curves 338 Chapter 6 Review Exercises 349 Part 3 Numerical Linear Algebra 551 _____ J Numerical Methods 353 Gaussian Elimination 353 The Method of LU Decomposition 359 Practical Difficulties in Solving Systems of Equations 366 Iterative Methods for Solving Systems of Linear Equations 375 Eigenvalues by Iteration and Connedivity of Networks 379 Chapter 7 Review Exercises 389 3 Linear Programming 391 A Geometrical Introduction to Linear Programming 391 The Simplex Method 399 tnPI Geometrical Explanation of the Simplex Method 405 Chapter 8 Review Exercises 411 Appendices 413 B3 Cross Produd 413 ВЭ Equations of Planes and Lines in Three-Space 423 Graphing Calculator Manual 431 Reduced Echelon Form of a Matrix (Sedions 1.1,1.2) 431 Matrix Operations (Sedions 2.1,2.2) 432 Powers of a Matrix (Sedions 2.2) 432 viii Contents Transpose of a Matrix (Sedion 2.3) 433 Inverse of a Matrix (Seđion 2.4) 433 Determinant of a Matrix (Seđion 3.1 ) 433 Summary of Formats for Row Operations (Sections 1.1,1.2) 434 MATLAB Manual 435 Entering and Displaying a Matrix (Seđion 1.1) 436 Solving Systems of Linear Equations (Seđions 1.1,1.2,1.6) 437 Dot Produd, Norm, Angle, Distance (Seđion 1.4) 441 Matrix Operations, Submatrices, Rows, and Columns (Seđions 2.1-2.3) 442 Computational Considerations (Seđion 2.2) 445 Inverse of a Matrix (Seđion 2.4) 446 Solving Systems of Equations Using Matrix Inverse (Seđion 2.4) 447 Cryptography (Seđion 2.4) 450 Transformations Defined by Matrices (Seđions 2.5,2.6) 451 Fractals (Seđion 2.6) 452 Leontief I/O Model (Seđion 2.7) 454 Markov Chains (Seđions 2.8,3.5) 456 Digraphs (Seđion 2.9) 458 Determinants (Seđions 3.1 -3.3) 460 Cramer s Rule (Seđion 3.3) 461 Eigenvalues, Eigenveđors, and Applications (Seđions 3.4,3.5) 463 Linear Combinations, Dependence, Basis, Rank (Seđions 1.3,4.2-4.4) 465 Projeđion, Gram-Schmidt Orthogonalization (Seđion 4.6) 468 Kernel and Range (Seđion 4.7) 469 Inner Produđ, Non-Euclidean Geometry (Seđions 6.1,6.2) 470 Space-Time Travel (Seđion 6.2) 473 Pseudoinverse and Least-Squares Curves (Seđion 6.4) 474 Contents ЕПЭ LU Decomposition (Sertion 7.2) 478 ΠΉΗ Condition Number of a Matrix (Section 7.3) 480 ΡΉ3 Jacobi and Gauss-Seidel Iterative Methods (Section 7.4) 481 ГТТЭ The Simplex Method in Linear Programming (Section 8.2) 483 РТУЗ Cross Product (Appendix A) 485 ΓΤΤΊ MATLAB Commands, Fundions, and M-files 486 ΡΤΤΠ The Linear Algebra with Applications Toolbox M-files 486 Answers to Selected Exercises 489 Index 535
adam_txt	Contents Preface xi Part 1 Linear Equations, Vectors, and Matrices 1_ f Linear Equations and Vectors 3 ED Matrices and Systems of Linear Equations 3 [Q Gauss-Jordan Elimination 15 The Vector Space R" 24 Basis and Dimension 33 Dot Product, Norm, Angle, and Distance 38 (Option: This section can be covered just before Section 4.6.) Curve Fitting, Electrical Networks, and Traffic Flow 49 Chapter 1 Review Exercises 57 2 Matrices and Linear Transformations 61 Addition, Scalar Multiplication, and Multiplication of Matrices 61 Properties of Matrix Operations 74 Symmetric Matrices and Sedation in Archaeology 85 The Inverse of a Matrix and Cryptography 95 Matrix Transformations, Rotations, and Dilations 108 Linear Transformations, Graphics, and Fractals 119 The Leontief Input-Output Model in Economics 129 'Sections marked with an asterisk are optional. The instructor can use these sections to build around the core material to give the course the desired flavor. vi Contents РП Markov Chains, Population Movements, and Genetics 135 И! A Communication Model and Group Relationships in Sociology 141 Chapter 2 Review Exercises 151 3 Determinants and Eigenvectors 155 Introduction to Determinants 155 Properties of Determinants 163 Determinants, Matrix Inverses, and Systems of Linear Equations 172 Eigenvalues and Eigenvectors 180 ff^ Google, Demography, and Weather Prediction (Option: Section 5.3, Diagonalization of Matrices, can be covered here.) 187 Chapter 3 Review Exercises 194 Part 2 Vector Spaces 197_ General Vector Spaces 199 ЕЖ1 General Veđor Spaces and Subspaces 199 СИ Linear Combinations 208 Linear Dependence and Independence 215 Properties of Bases 220 Rank 228 Orthonormal Vectors and Projections 237 Kernel, Range, and the Rank/Nullity Theorem 249 One-to-One Transformations and Inverse Transformations 259 Transformations and Systems of Linear Equations 264 Chapter 4 Review Exercises 271 5 Coordinate Representations 275 Coordinate Vectors 275 Matrix Representations of Linear Transformations 283 Diagonalization of Matrices 292 Contents vii Quadratic Forms, Difference Equations, and Normal Modes 303 Chapter 5 Review Exercises 314 jjj Inner Product Spaces 317 Inner Product Spaces 317 Non-Euclidean Geometry and Special Relativity 326 Approximation of Fundions and Coding Theory 331 Least Squares Curves 338 Chapter 6 Review Exercises 349 Part 3 Numerical Linear Algebra 551 _ 'J Numerical Methods 353 Gaussian Elimination 353 The Method of LU Decomposition 359 Practical Difficulties in Solving Systems of Equations 366 Iterative Methods for Solving Systems of Linear Equations 375 Eigenvalues by Iteration and Connedivity of Networks 379 Chapter 7 Review Exercises 389 3 Linear Programming 391 A Geometrical Introduction to Linear Programming 391 The Simplex Method 399 tnPI Geometrical Explanation of the Simplex Method 405 Chapter 8 Review Exercises 411 Appendices 413 B3 Cross Produd 413 ВЭ Equations of Planes and Lines in Three-Space 423 Graphing Calculator Manual 431 Reduced Echelon Form of a Matrix (Sedions 1.1,1.2) 431 Matrix Operations (Sedions 2.1,2.2) 432 Powers of a Matrix (Sedions 2.2) 432 viii Contents Transpose of a Matrix (Sedion 2.3) 433 Inverse of a Matrix (Seđion 2.4) 433 Determinant of a Matrix (Seđion 3.1 ) 433 Summary of Formats for Row Operations (Sections 1.1,1.2) 434 MATLAB Manual 435 Entering and Displaying a Matrix (Seđion 1.1) 436 Solving Systems of Linear Equations (Seđions 1.1,1.2,1.6) 437 Dot Produd, Norm, Angle, Distance (Seđion 1.4) 441 Matrix Operations, Submatrices, Rows, and Columns (Seđions 2.1-2.3) 442 Computational Considerations (Seđion 2.2) 445 Inverse of a Matrix (Seđion 2.4) 446 Solving Systems of Equations Using Matrix Inverse (Seđion 2.4) 447 Cryptography (Seđion 2.4) 450 Transformations Defined by Matrices (Seđions 2.5,2.6) 451 Fractals (Seđion 2.6) 452 Leontief I/O Model (Seđion 2.7) 454 Markov Chains (Seđions 2.8,3.5) 456 Digraphs (Seđion 2.9) 458 Determinants (Seđions 3.1 -3.3) 460 Cramer's Rule (Seđion 3.3) 461 Eigenvalues, Eigenveđors, and Applications (Seđions 3.4,3.5) 463 Linear Combinations, Dependence, Basis, Rank (Seđions 1.3,4.2-4.4) 465 Projeđion, Gram-Schmidt Orthogonalization (Seđion 4.6) 468 Kernel and Range (Seđion 4.7) 469 Inner Produđ, Non-Euclidean Geometry (Seđions 6.1,6.2) 470 Space-Time Travel (Seđion 6.2) 473 Pseudoinverse and Least-Squares Curves (Seđion 6.4) 474 Contents ЕПЭ LU Decomposition (Sertion 7.2) 478 ΠΉΗ Condition Number of a Matrix (Section 7.3) 480 ΡΉ3 Jacobi and Gauss-Seidel Iterative Methods (Section 7.4) 481 ГТТЭ The Simplex Method in Linear Programming (Section 8.2) 483 РТУЗ Cross Product (Appendix A) 485 ΓΤΤΊ MATLAB Commands, Fundions, and M-files 486 ΡΤΤΠ The Linear Algebra with Applications Toolbox M-files 486 Answers to Selected Exercises 489 Index 535
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spelling	Williams, Gareth Verfasser aut Linear algebra with applications Gareth Williams 6. ed. Boston [u.a.] Jones and Bartlett 2008 XVI, 544 S.t. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015959245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Williams, Gareth Linear algebra with applications Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd
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title	Linear algebra with applications
title_auth	Linear algebra with applications
title_exact_search	Linear algebra with applications
title_exact_search_txtP	Linear algebra with applications
title_full	Linear algebra with applications Gareth Williams
title_fullStr	Linear algebra with applications Gareth Williams
title_full_unstemmed	Linear algebra with applications Gareth Williams
title_short	Linear algebra with applications
title_sort	linear algebra with applications
topic	Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd
topic_facet	Algebras, Linear Textbooks Lineare Algebra
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015959245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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