Linear Algebra with Applications
Pearson (Verlag)
978-0-13-033781-8 (ISBN)
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Written for undergraduate first courses in Linear Algebra. Assumes the user has had calculus.
Renowned for thoroughness and accessibility, this top-selling text by one of the leading figures in linear algebra education offers students a challenging and enjoyable study of linear algebra that is infused with an abundance of applications. Balancing coverage of mathematical theory and applied topics, Professor Leon explains concepts with precision so that students at any level can understand the material. Worked examples are heavily integrated into each chapter. The book stresses the important role geometry and visualization play in understanding the subject. This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides.
(*The Supplemental Chapters 8 and 9 can be downloaded from the web page.)
1. Matrices and Systems of Equations.
Systems of Linear Equations. Row Echelon Form. Matrix Algebra. Elementary Matrices. Partitioned Matrices. Matlab Exercises. Chapter Test.
2. Determinants.
The Determinant of a Matrix. Properties of Determinants. Cramer's Rule. Matlab Exercises. Chapter Test.
3. Vector Spaces.
Definition and Examples. Subspaces. Linear Independence. Basis and Dimension. Change of Basis. Row Space and Column Space. Matlab Exercises. Chapter Test.
4. Linear Transformations.
Definition and Examples. Matrix Representations of Linear Transformations. Similarity. Matlab Exercises. Chapter Test.
5. Orthogonality.
The Scalar Product in Rn. Orthogonal Subspaces. Least Squares Problems. Inner Product Spaces. Orthonormal Sets. The Gram-Schmidt Orthogonalization Process. Orthogonal Polynomials. Matlab Exercises. Chapter Test.
6. Eigenvalues.
Eigenvalues and Eigenvectors. Systems of Linear Differential Equations. Diagonalization. Hermitian Matrices. The Singular Value Decomposition. Quadratic Forms. Positive Definite Matrices. Nonnegative Matrices. Matlab Exercises. Chapter Test.
7. Numerical Linear Algebra.
Floating-Point Numbers. Gaussian Elimination. Pivoting Strategies. Matrix Norms and Condition Numbers. Orthogonal Transformations. The Eigenvalue Problem. Least Squares Problems. Matlab Exercises. Chapter Test.
*8. Iterative Methods.
*9. Jordan Canonical Form.
Appendix: MATLAB.
Bibliography.
Answers to Selected Exercises.
Index.
| Erscheint lt. Verlag | 7.3.2002 |
|---|---|
| Sprache | englisch |
| Maße | 181 x 242 mm |
| Gewicht | 956 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-13-033781-1 / 0130337811 |
| ISBN-13 | 978-0-13-033781-8 / 9780130337818 |
| Zustand | Neuware |
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