Introductory Linear Algebra with Applications: An Applied First Course

74 Pages·2001·0.658 MB·English

by  Kolman, B, Hill, D

I
NTRODUCTORY
L A
INEAR LGEBRA
AN APPLIED FIRST COURSE

E I G H T H E D I T I O N
I
NTRODUCTORY
L A
INEAR LGEBRA
AN APPLIED FIRST COURSE
Bernard Kolman
DrexelUniversity
David R. Hill
TempleUniversity
UpperSaddleRiver,NewJersey07458
LibraryofCongressCataloging-in-PublicationData
Kolman,Bernard,Hill,DavidR.
Introductorylinearalgebra:anappliedfirstcourse-8thed./BernardKolman,DavidR.Hill
p.cm.
Rev.ed.of:Introductorylinearalgebrawithapplications.7thed.c2001.
Includesbibliographicalreferencesandindex.
ISBN0-13-143740-2
1.Algebras,Linear. I.Hill,DavidR.II.Kolman,Bernard.Introductorylinearalgebra
withapplications.III.Title.
QA184.2.K65 2005
512'.5--dc22 2004044755
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• •
To the memory of Lillie
and to Lisa and Stephen
B.K.
To Suzanne
D.R.H.
• •

C
ONTENTS
Preface xi
TotheStudent xix
1
Linear Equations and Matrices 1
1.1 LinearSystems 1
1.2 Matrices 10
1.3 DotProductandMatrixMultiplication 21
1.4 PropertiesofMatrixOperations 39
1.5 MatrixTransformations 52
1.6 SolutionsofLinearSystemsofEquations 62
1.7 TheInverseofaMatrix 91
1.8 LU-Factorization(Optional) 107
2
Applications of Linear Equations
and Matrices (Optional) 119
2.1 AnIntroductiontoCoding 119
2.2 GraphTheory 125
2.3 ComputerGraphics 135
2.4 ElectricalCircuits 144
2.5 MarkovChains 149
2.6 LinearEconomicModels 159
2.7 IntroductiontoWavelets 166
3
Determinants 182
3.1 DefinitionandProperties 182
3.2 CofactorExpansionandApplications 196
3.3 DeterminantsfromaComputationalPointofView 210
4 Vectors in Rn 214
4.1 VectorsinthePlane 214
4.2 n-Vectors 229
4.3 LinearTransformations 247
vii
viii Contents
5 Applications of Vectors in R2
and R3 (Optional) 259
5.1 CrossProductin R3 259
5.2 LinesandPlanes 264
6
Real Vector Spaces 272
6.1 VectorSpaces 272
6.2 Subspaces 279
6.3 LinearIndependence 291
6.4 BasisandDimension 303
6.5 HomogeneousSystems 317
6.6 TheRankofaMatrixandApplications 328
6.7 CoordinatesandChangeofBasis 340
6.8 OrthonormalBasesin Rn 352
6.9 OrthogonalComplements 360
7
Applications of Real Vector
Spaces (Optional) 375
7.1 QR-Factorization 375
7.2 LeastSquares 378
7.3 MoreonCoding 390
8
Eigenvalues, Eigenvectors, and
Diagonalization 408
8.1 EigenvaluesandEigenvectors 408
8.2 Diagonalization 422
8.3 DiagonalizationofSymmetricMatrices 433
9
Applications of Eigenvalues and
Eigenvectors (Optional) 447
9.1 TheFibonacciSequence 447
9.2 DifferentialEquations(CalculusRequired) 451
9.3 DynamicalSystems(CalculusRequired) 461
9.4 QuadraticForms 475
9.5 ConicSections 484
9.6 QuadricSurfaces 491
10
Linear Transformations and Matrices 502
10.1 DefinitionandExamples 502
10.2 TheKernelandRangeofaLinearTransformation 508
10.3 TheMatrixofaLinearTransformation 521
10.4 IntroductiontoFractals(Optional) 536
Cumulative Review of
Introductory Linear Algebra 555
Contents ix
11
Linear Programming (Optional) 558
11.1 TheLinearProgrammingProblem;GeometricSolution 558
11.2 TheSimplexMethod 575
11.3 Duality 591
11.4 TheTheoryofGames 598
12
MATLAB for Linear Algebra 615
12.1 InputandOutputinMATLAB 616
12.2 MatrixOperationsinMATLAB 620
12.3 MatrixPowersandSomeSpecialMatrices 623
12.4 ElementaryRowOperationsinMATLAB 625
12.5 MatrixInversesinMATLAB 634
12.6 VectorsinMATLAB 635
12.7 ApplicationsofLinearCombinationsinMATLAB 637
12.8 LinearTransformationsinMATLAB 640
12.9 MATLABCommandSummary 643
A
APPENDIX Complex Numbers A1
A.1 ComplexNumbers A1
A.2 ComplexNumbersinLinearAlgebra A9
B
APPENDIX Further Directions A19
B.1 InnerProductSpaces(CalculusRequired) A19
B.2 CompositeandInvertibleLinearTransformations A30
Glossary for Linear Algebra A39
Answers to Odd-Numbered Exercises
and Chapter Tests A45
Index I1