Linear algebra and its applications
著者
書誌事項
Linear algebra and its applications
Addison-Wesley, c2000
2nd ed update
- Student resource disk
- : Instructor's ed.
大学図書館所蔵 全3件
注記
Includes index
Each volume accompanies 1 computer laser optical discs
内容説明・目次
内容説明
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a "brick wall." Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible. Students' conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology.
David Lay changed the face of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition. With this update, he builds on this philosophy through increased visualization in the text, vastly enhanced technology support, and an extensive instructor support package. He has added additional figures to the text to help students visualize abstract concepts at key points in the course. A new dedicated CD and Website further enhance the course materials by providing additional support to help students gain command of difficult concepts. The CD, included in the back of the book, contains a wealth of new materials, with a registration coupon allowing access to a password-protected Website. These new materials are tied directly to the text, providing a comprehensive package for teaching and learning linear algebra.
目次
- (Each chapter begins with an Introductory Example and ends with Supplementary Exercises.) 1. Linear Equations In Linear Algebra. Introductory Example: Linear Models in Economics and Engineering. Systems of Linear Equations. Row Reduction and Echelon Forms. Vector Equations. The Matrix Equation Ax = b. Solution Sets of Linear Systems. Linear Independence. Introduction to Linear Transformations. The Matrix of a Linear Transformation. Linear Models in Business, Science, and Engineering. Supplementary Exercises . 2. Matrix Algebra. Introductory Example: Computer Graphics in Automotive Design. Matrix Operations. The Inverse of a Matrix. Characterizations of Invertible Matrices. Partitioned Matrices. Matrix Factorizations. Iterative Solutions of Linear Systems. The Leontief Input-Output Model. Applications to Computer Graphics. Subspaces of Rn. Supplementary Exercises . 3. Determinants. Introductory Example: Determinants in Analytic Geometry. Introduction to Determinants. Properties of Determinants. Cramers Rule, Volume, and Linear Transformations. Supplementary Exercises. 4. Vector Spaces. Introductory Example: Space Flight and Control Systems. Vector Spaces and Subspaces. Null Spaces, Column Spaces, and Linear Transformations. Linearly Independent Sets
- Bases. Coordinate Systems. The Dimension of a Vector Space. Rank. Change of Basis. Applications to Difference Equations. Applications to Markov Chains. Supplementary Exercises. 5. Eigenvalues and Eigenvectors. Introductory Example: Dynamical Systems and Spotted Owls. Eigenvectors and Eigenvalues. The Characteristic Equation. Diagonalization. Eigenvectors and Linear Transformations. Complex Eigenvalues. Discrete Dynamical Systems. Applications to Differential Equations. Iterative Estimates for Eigenvalues. Supplementary Exercises. 6. Orthogonality and Least-Squares. Introductory Example: Readjusting the North American Datum. Inner Product, Length, and Orthogonality. Orthogonal Sets. Orthogonal Projections. The Gram-Schmidt Process. Least-Squares Problems. Applications to Linear Models. Inner Product Spaces. Applications of Inner Product Spaces. Supplementary Exercises. 7. Symmetric Matrices and Quadratic Forms. Introductory Example: Multichannel Image Processing. Diagonalization of Symmetric Matrices. Quadratic Forms. Constrained Optimization. The Singular Value Decomposition. Applications to Image Processing and Statistics. Supplementary Exercises. Appendices. Uniqueness of the Reduced Echelon Form. Complex Numbers. Glossary. Answers to Odd-Numbered Exercises. Index.
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