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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 선형대수학
· ISBN : 9780471682998
· 쪽수 : 550쪽
· 출판일 : 2005-03-01
목차
Chapter 1 Systems of Linear Equations 1
1.1 Solving Linear Systems 2
1.2 Geometric Perspectives on Linear Systems 18
1.3A Solving Linear Systems Using Maple 26
1.3B Solving Linear Systems Using Mathematics 36
1.4 Curve Fitting and Temperature Distribution-Application 45
Chapter 2 Vectors 56
2.1 Geometry of Vectors 57
2.2 Linear Combinations of Vectors 71
2.3 Decomposing the Solution of a Linear System 84
2.4 Linear Independence of Vectors 92
2.5 Theory of Vector Concepts 106
Chapter 3 Matrix Algebra 113
3.1 Product of a Matrix and a Vector 114
3.2 Matrix Multiplication 125
3.3 Rules of Matrix Algebra 140
3.4 Markov Chains-Application 147
3.5 Inverse of a Matrix 161
3.6 Theory of Matrix Inverses 175
3.7 Cryptology-Application 180
Chapter 4 Linear Transformations 193
4.1 Introduction to Matrix Transformations 194
4.2 Geometry of Matrix Transformations of the Plane 198
4.3 Geometry of Matrix Transformations of 3-Space 220
4.4 Linear Transformations 232
4.5 Computer Graphics-Applications 237
Chapter 5 Vector Spaces 255
5.1 Subspaces of Rᴺ 256
5.2 Basis and Dimension 262
5.3 Theory of Basis and Dimension 272
5.4 Subspaces Associated with a Matrix 275
5.5 Theory of Subspaces Associated with a Matrix 285
5.6 Loops and Spanning Trees-Application 289
5.7 Abstract Vector Spaces 297
Chapter 6 Determinants 306
6.1 Determinants and Cofactors 307
6.2 Properties of Determinants 311
6.3 Theory of Determination 322
Chapter 7 Eigenvalues and Eigenvectors 328
7.1 Introduction to Eigenvalues and Eigenvectors 329
7.2 The Characteristics Polynomial 343
7.3 Discrete Dynamical Systems-Application 356
7.4 Diagonalization and Similar Matrices 373
7.5 Theory of Eigenvalues and Eigenvectors 389
7.6 Systems of Linear Differential Equations-Application 395
7.7 Complex Numbers and Complex Vectors 407
7.8 Complex Eigenvalue and Eigenvectors 411
Chapter 8 Orthogonality 431
8.1 Dot Product and Orthogonal Vectors 432
8.2 Orthogonal Projections in R² and R³ 437
8.3 Orthogonal Projections and Orthogonal Bases in Rᴺ 447
8.4 Theory of Orthogonality 456
8.5 Least-Squares Solution-Application 463
8.6 Weighted Least-Squares and Inner Products on Rᴺ 475
8.7 Approximation of Functions and Integral Inner Products 483
8.8 Inner Product Spaces 496
Appendix A Glossary of Linear Algebra Definitions 503
Appendix B Linear Algebra Theorems 510
Appendix C Advice for Using Maple with Visual Linear Algebra 519
Appendix D Commands Used in Maple Tutorials 521
Appendix E Advice for Using Mathematica with Visual Linear Algebra 527
Appendix F Commands Used in Mathematica Tutorials 530
Appendix G Answers and Hints for Selected Pencil and Paper Problems 537
Index 545
