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Linear algebra and its applications 2nd ed. update

Linear algebra and its applications 2nd ed. update (Loan 29 times)

Material type
단행본
Personal Author
Lay, David C.
Title Statement
Linear algebra and its applications / David C. Lay.
판사항
2nd ed. update.
Publication, Distribution, etc
Reading, Mass. :   Addison-Wesley,   c2000.  
Physical Medium
1 v. (various pagings) : ill. ; 24 cm. + 1 computer optical disc (4 3/4 in.).
ISBN
0201347741 0201648458(Instructor's Edition)
Bibliography, Etc. Note
Includes bibliographical references and index.
Subject Added Entry-Topical Term
Algebras, Linear.
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008 990618s2000 maua b 001 0 eng
010 ▼a 99037547
020 ▼a 0201347741
020 ▼a 0201648458(Instructor's Edition)
040 ▼a DLC ▼c DLC ▼d C#P ▼d 211009
049 1 ▼l 121051125 ▼f 과학
050 0 0 ▼a QA184 ▼b .L397 2000
082 0 0 ▼a 512/.5 ▼2 21
090 ▼a 512.5 ▼b L426L2
100 1 ▼a Lay, David C.
245 1 0 ▼a Linear algebra and its applications / ▼c David C. Lay.
250 ▼a 2nd ed. update.
260 ▼a Reading, Mass. : ▼b Addison-Wesley, ▼c c2000.
300 ▼a 1 v. (various pagings) : ▼b ill. ; ▼c 24 cm. + ▼e 1 computer optical disc (4 3/4 in.).
504 ▼a Includes bibliographical references and index.
538 ▼a System requirements: Windows 95, 98, NT or Macintosh System 7.2; 640x480x256 color display; 28.8 Mhz modem; Internet Explorer 4.0 or Netscape 4.0 (available on CD-ROM); Adobe Acrobat Reader 4.0 (available on CD-ROM); WinZip 7.0 or StuffIt Expander 5.0 (both available on the CD-ROM).
650 0 ▼a Algebras, Linear.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.5 L426L2 Accession No. 121051125 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS

PREFACE = xiii

A NOTE TO STUDENTS = xix

1 LINEAR EQUATIONS IN LINEAR ALGEBRA = 1

 Introductory Example : Linear Models in Economics and Engineering = 1

 1.1 Systems of Linear Equations = 2

 1.2 Row Reduction and Echelon Forms = 13

 1.3 Vector Equations = 27

 1.4 The Matrix Equation Ax=b = 39

 1.5 Solution Sets of Linear Systems = 48

 1.6 Linear Independence = 58

 1.7 Introduction to Linear Transformations = 66

 1.8 The Matrix of d Linear Transformation = 76

 1.9 Linear Models in Business Science, and Engineering = 85

 Supplementary Exercises = 95

2 MATRIX ALGEBRA = 97

 Introductory Example : Computer Graphics in Automotive Design = 97

 2.1 Matrix Operations = 98

 2.2 The Inverse of a Matrix = 110

 2.3 Characterizations of Invertible Matrices = 120

 2.4 Partitioned Matrices = 125

 2.5 Matrix Factorizations = 133

 2.6 Iterative Solutions of Linear Systems = 143

 2.7 The Leontief Input-Output Mode1 = 148

 2.8 Applications to Computer Graphics = 155

 2.9 Subspaces of $$R^n$$ = 165

 Supplementary Exercises = 177

3 DETERMINANTS = 179

 Introductory Example : Determinants in Analytic Geometry = 179

 3.1 Introduction to Determinants = 180

 3.2 Properties of Determinants = 187

 3.3 Cramer's Rule, Volume, and Linear Transformations = 195

 Supplementary Exercises = 206

4 VECTOR SPACES = 209

 Introductory Example : Space Flight and Control Systems = 209

 4.1 Vector Spaces and Subspaces = 210

 4.2 Null Spaces, Column Spaces, and Linear Transformations = 220

 4.3 Linearly Independent Sets : Bases = 231

 4.4 Coordinate Systems = 240

 4.5 The Dimension of a Vector Space = 250

 4.6 Rank = 257

 4.7 Change of Basis = 265

 4.8 Applications to Difference Equations = 271

 4.9 Applications to Markov Chains = 282

 Supplementary Exercises = 292

5 EIGENVALUES AND EIGENVECTORS = 295

 Introductory Example : Dynamical Systems and Spotted Owls = 295

 5.1 Eigenvectors and Eigenvalues = 296

 5.2 The Characteristic Equation = 305

 5.3 Diagonalization = 313

 5.4 Eigenvectors and Linear Transformations = 321

 5.5 Complex Eigenvalues = 329

 5.6 Discrete Dynamical Systems = 336

 5.7 Applications to Differential Equations = 347

 5.8 Iterative Estimates for Eigenvalues = 357

 Supplementary Exercises = 365

6 ORTHOGONALITY AND LEAST-SQUARES = 367

 Introductory Example : Readjusting the North American Datum = 367

 6.1 Inner Product, Length, and Orthogonality = 369

 6.2 Orthogonal Sets = 378

 6.3 Orthogonal Projections = 389

 6.4 The Gram-Schmidt Process = 397

 6.5 Least-Squares Problems = 404

 6.6 Applications to Linear Models = 414

 6.7 Inner Product Spaces = 422

 6.8 Applications of Inner Product Spaces = 431

 Supplementary Exercises = 439

7 SYMMETRIC MATRICES AND QUADRATIC FORMS = 441

 Introductory Example : Multichannel Image Processing = 441

 7.1 Diagonalization of Symmetric Matrices = 443

 7.2 Quadratic Forms = 450

 7.3 Constrained Optimization = 458

 7.4 The Singular Value Decomposition = 466

 7.5 Applications to Image Processing and Statistics = 477

 Supplementary Exercises = 485

Appendixes

 A Uniqueness of the Reduced Echelon Form = A1

 B Complex Numbers = A3

Glossary = A9

Answers to Odd-Numbered Exercises = A21

Index = I1



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