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Genre/Form: | Textbooks |
---|---|
Document Type: | Book |
All Authors / Contributors: |
Howard Anton |
ISBN: | 9780470458211 0470458216 9780470432051 0470432055 |
OCLC Number: | 463637219 |
Notes: | Includes index. |
Description: | xv, 568 pages : illustrations ; 27 cm |
Contents: | 1. Systems of liner equations and matrices -- Introduction to systems of linear equations -- Gaussian elimination -- Matrices and matrix operations -- Inverses -- Algebraic properties of matrices -- Elementary matrices -- More on linear systems and invertible matrices -- Diagonal, triangular, and symmetric matrices -- Applications of linear systems -- Leontief input-output models -- 2. Determinants -- Cofactor expansion -- Row reduction -- Cramer's Rule -- 3. Euclidean vector spaces -- Vectors in 2-Space, 3-Space and n-Space -- Norm, dot product, and distance in Rn -- Orthogonality -- Geometry of linear systems -- Cross product -- 4. General vector spaces -- Real vector spaces -- Subspaces -- Linear independence -- Coordinates and basis -- Dimension -- Change of basis -- Row space, column space, and null space -- Rank, nullity, and the fundamental matrix spaces -- Matrix transformations -- Geometry of matrix operators -- Dynamical systems and Markov Chains -- 5. Eigenvalues and eigenvectors -- Eigenvalues and eigenvectors -- Diagonalization -- Complex vector spaces -- Differential equations -- 6. Inner product spaces -- Inner products -- Angel and orthogonality in inner product spaces -- Gram-Schmidt Process -- QR-decomposition -- Best approximation -- Least squares -- Least squares fitting to data -- Function approximation -- Fourier Series -- 7. Diagonalization and quadratic forms -- Orthogonal matrices -- Orthogonal diagonalization -- Quadratic forms -- Optimization using quadratic forms -- Hermitian, unitary, and normal matrices -- 8. Linear transformations -- General linear transformations -- Isomorphism -- Compositions and inverse transformations -- Matrices for general linear transformations -- Similarity -- 9. Numerical methods -- LU-decompositions -- The power method -- Internet search engines -- Comparison of procedures for solving linear systems -- Singular value decomposition -- Data compression using singular value decomposition -- Appendix A. How to read theorems -- Appendix B. Complex numbers. |
Responsibility: | Howard Anton. |
Abstract:
Offers an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. This title intends to present the fundamentals of linear algebra.
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