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| Material Type: | Internet resource |
|---|---|
| Document Type: | Book, Internet Resource |
| All Authors / Contributors: |
David C Lay |
| ISBN: | 0321287134 9780321287137 0321314859 9780321314857 |
| OCLC Number: | 835590726 |
| Description: | Getr. Zählung Illustrationen, Diagramme 1 CD-ROM |
| Contents: | Chapter 1 Linear Equations in Linear Algebra INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering 1.1 Systems of Linear Equations1.2 Row Reduction and Echelon Forms1.3 Vector Equations1.4 The Matrix Equation Ax = b1.5 Solution Sets of Linear Systems1.6 Applications of Linear Systems1.7 Linear Independence1.8 Introduction to Linear Transformations1.9 The Matrix of a Linear Transformation1.10 Linear Models in Business, Science, and Engineering Supplementary Exercises Chapter 2 Matrix Algebra INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design 2.1 Matrix Operations2.2 The Inverse of a Matrix2.3 Characterizations of Invertible Matrices2.4 Partitioned Matrices2.5 Matrix Factorizations2.6 The Leontief Input=Output Model2.7 Applications to Computer Graphics2.8 Subspaces of R^n2.9 Dimension and Rank Supplementary Exercises Chapter 3 Determinants INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry 3.1 Introduction to Determinants3.2 Properties of Determinants3.3 Cramer's Rule, Volume, and Linear Transformations Supplementary Exercises Chapter 4 Vector Spaces INTRODUCTORY EXAMPLE: Space Flight and Control Systems 4.1 Vector Spaces and Subspaces4.2 Null Spaces, Column Spaces, and Linear Transformations4.3 Linearly Independent Sets; Bases4.4 Coordinate Systems4.5 The Dimension of a Vector Space4.6 Rank4.7 Change of Basis4.8 Applications to Difference Equations4.9 Applications to Markov Chains Supplementary Exercises Chapter 5 Eigenvalues and Eigenvectors INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls 5.1 Eigenvectors and Eigenvalues5.2 The Characteristic Equation5.3 Diagonalization5.4 Eigenvectors and Linear Transformations5.5 Complex Eigenvalues5.6 Discrete Dynamical Systems5.7 Applications to Differential Equations5.8 Iterative Estimates for Eigenvalues Supplementary Exercises Chapter 6 Orthogonality and Least Squares INTRODUCTORY EXAMPLE: Readjusting the North American Datum 6.1 Inner Product, Length, and Orthogonality6.2 Orthogonal Sets6.3 Orthogonal Projections6.4 The Gram-Schmidt Process6.5 Least-Squares Problems6.6 Applications to Linear Models6.7 Inner Product Spaces6.8 Applications of Inner Product Spaces Supplementary Exercises Chapter 7 Symmetric Matrices and Quadratic Forms INTRODUCTORY EXAMPLE: Multichannel Image Processing 7.1 Diagonalization of Symmetric Matrices7.2 Quadratic Forms7.3 Constrained Optimization7.4 The Singular Value Decomposition7.5 Applications to Image Processing and Statistics Supplementary Exercises ONLINE ONLY Chapter 8 The Geometry of Vector Spaces INTRODUCTORY EXAMPLE: The Platonic Solids 8.1 Affine Combinations8.2 Affine Independence8.3 Convex Combinations8.4 Hyperplanes8.5 Polytopes8.6 Curves and Surfaces Supplementary Exercises ONLINE ONLY Chapter 9 Optimization INTRODUCTORY EXAMPLE: The Berlin Airlift 9.1 Matrix Games9.2 Linear Programming - Geometric Method9.3 Linear Programming - Simplex Method9.4 Duality Supplementary Exercises Appendices A Uniqueness of the Reduced Echelon FormB Complex Numbers Glossary Answers to Odd-Numbered Exercises Index |
| Responsibility: | David C. Lay |
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