Linear Algebra

with Applications

Jeffrey Holt (Autor)

Buch | Hardcover

912 Seiten

2016 | 2nd ed. 2017
W.H.Freeman & Co Ltd (Verlag)
978-1-4641-9334-7 (ISBN)

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Now in its 2nd edition, Linear Algebra with Applications blends computational and conceptual topics to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation.

Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce topics. The text also has over 2500 exercises, covering computational and conceptual topics over a range of difficulty levels.

Jeffrey Holt has a B.A. from Humboldt State University and a Ph.D. from the University of Texas. He has been teaching mathematics for over 20 years, the last eleven at the University of Virginia. He currently has a joint appointment in the Department of Mathematics and the Department of Statistics at UVA.

1. Systems of Linear Equations.- 1.1 Lines and Linear Equations.- 1.2 Linear Systems and Matrices.- 1.3 Applications of Linear Systems
1.4 Numerical Solutions.- 2. Euclidean Space.- 2.1 Vectors.- 2.2 Span.- 2.3 Linear Independence.- 3. Matrices.- 3.1 Linear Transformations.- 3.2 Matrix Algebra.- 3.3 Inverses.- 3.4 LU Factorization.- 3.5 Markov Chains.- 4. Subspaces.- 4.1 Introduction to Subspaces.- 4.2 Basis and Dimension.- 4.3 Row and Column Spaces.- 4.4 Change of Basis.- 5. Determinants.- 5.1 The Determinant Function.- 5.2 Properties of the Determinant.- 5.3 Applications of the Determinant.- 6. Eigenvalues and Eigenvectors.- 6.1 Eigenvalues and Eigenvectors.- 6.2 Diagonalization.- 6.3 Complex Eigenvalues and Eigenvectors.- 6.4 Systems of Differential Equations .- 6.5 Approximation Methods.- 7. Vector Spaces.- 7.1 Vector Spaces and Subspaces.- 7.2 Span and Linear Independence.- 7.3 Basis and Dimension.- 8. Orthogonality.- 8.1 Dot Products and Orthogonal Sets.- 8.2 Projection and the Gram-Schmidt Process.- 8.3 Diagonalizing Symmetric Matrices and QR Factorization
8.4 The Singular Value Decomposition.- 8.5 Least Squares Regression.- 9. Linear Transformations.- 9.1 Definition and Properties.- 9.2 Isomorphisms.- 9.3 The Matrix of a Linear Transformation.- 9.4 Similarity.- 10. Inner Product Spaces.- 10.1 Inner Products.- 10.2 The Gram-Schmidt Process Revisited.- 10.3 Applications of Inner Products.- 11. Additional Topics and Applications.- 11.1 Quadratic Forms.- 11.2 Positive Definite Matrices.- 11.3 Constrained Optimization.- 11.4 Complex Vector Spaces.- 11.5 Hermitian Matrices.- Glossary.- Answers to Selected Exercises.- Index

Erscheinungsdatum	24.01.2017
Zusatzinfo	912 p.
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	1-4641-9334-7 / 1464193347
ISBN-13	978-1-4641-9334-7 / 9781464193347
Zustand	Neuware