Contemporary linear algebra
著者
書誌事項
Contemporary linear algebra
Wiley, c2003
大学図書館所蔵 全40件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
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  オランダ
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注記
Includes index
内容説明・目次
内容説明
From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without sacrificing mathematical precision, Anton and Busby focus on the aspects of linear algebra that are most likely to have practical value to the student while not compromising the intrinsic mathematical form of the subject. Throughout Contemporary Linear Algebra, students are encouraged to look at ideas and problems from multiple points of view.
目次
- CHAPTER 1 Vectors 1 1.1 Vectors and Matrices in Engineering and Mathematics
- n-Space 1 1.2 Dot Product and Orthogonality 15 1.3 Vector Equations of Lines and Planes 29 CHAPTER 2 Systems of Linear Equations 39 2.1 Introduction to Systems of Linear Equations 39 2.2 Solving Linear Systems by Row Reduction 48 2.3 Applications of Linear Systems 63 CHAPTER 3 Matrices and Matrix Algebra 79 3.1 Operations on Matrices 79 3.2 Inverses
- Algebraic Properties of Matrices 94 3.3 Elementary Matrices
- A Method for Finding A 1 109 3.4 Subspaces and Linear Independence 123 3.5 The Geometry of Linear Systems 135 3.6 Matrices with Special Forms 143 3.7 Matrix Factorizations
- LU-Decomposition 154 3.8 Partitioned Matrices and Parallel Processing 166 CHAPTER 4 Determinants 175 4.1 Determinants
- Cofactor Expansion 175 4.2 Properties of Determinants 184 4.3 Cramer's Rule
- Formula for A 1
- Applications of Determinants 196 4.4 A First Look at Eigenvalues and Eigenvectors 210 CHAPTER 5 Matrix Models 225 5.1 Dynamical Systems and Markov Chains 225 5.2 Leontief Input-Output Models 235 5.3 Gauss-Seidel and Jacobi Iteration
- Sparse Linear Systems 241 5.4 The Power Method
- Application to Internet Search Engines 249 CHAPTER 6 Linear Transformations 265 6.1 Matrices as Transformations 265 6.2 Geometry of Linear Operators 280 6.3 Kernel and Range 296 6.4 Composition and Invertibility of Linear Transformations 305 6.5 Computer Graphics 318 CHAPTER 7 Dimension and Structure 329 7.1 Basis and Dimension 329 7.2 Properties of Bases 335 7.3 The Fundamental Spaces of a Matrix 342 7.4 The Dimension Theorem and Its Implications 352 7.5 The Rank Theorem and Its Implications 360 7.6 The Pivot Theorem and Its Implications 370 7.7 The Projection Theorem and Its Implications 379 7.8 Best Approximation and Least Squares 393 7.9 Orthonormal Bases and the Gram-Schmidt Process 406 7.10 QR-Decomposition
- Householder Transformations 417 7.11 Coordinates with Respect to a Basis 428 CHAPTER 8 Diagonalization 443 8.1 Matrix Representations of Linear Transformations 443 8.2 Similarity and Diagonalizability 456 8.3 Orthogonal Diagonalizability
- Functions of a Matrix 468 8.4 Quadratic Forms 481 8.5 Application of Quadratic Forms to Optimization 495 8.6 Singular Value Decomposition 502 8.7 The Pseudoinverse 518 8.8 Complex Eigenvalues and Eigenvectors 525 8.9 Hermitian, Unitary, and Normal Matrices 535 8.10 Systems of Differential Equations 542 CHAPTER 9 General Vector Spaces 555 9.1 Vector Space Axioms 555 9.2 Inner Product Spaces
- Fourier Series 569 9.3 General Linear Transformations
- Isomorphism 582 APPENDIX A How to Read Theorems A1 APPENDIX B Complex Numbers A3 ANSWERS TO ODD-NUMBERED EXERCISES A9 PHOTO CREDITS C1 INDEX I-1
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