(EBOOK PDF)Linear Algebra in Action 2nd Edition by Harry Dym 9781470409081 1470409089 full chapters

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Product details:

• ISBN 10:1470409089  

• ISBN 13:9781470409081

• Author:Harry Dym 

  Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.
                                                                                                                                               

Linear Algebra in Action 2nd Table of contents:

Preface to the Second Edition
Preface to the First Edition
1. Vector spaces
2. Gaussian elimination
3. Additional applications of Gaussian elimination
4. Eigenvalues and eigenvectors
5. Determinants
6. Calculating Jordan forms
7. Normed linear spaces
8. Inner product spaces and orthogonality
9. Symmetric, Hermitian and normal matrices
10. Singular values and related inequalities
11. Pseudoinverses
12. Triangular factorization and positive definite matrices
13. Difference equations and differential equations
14. Vector-valued functions
15. The implicit function theorem
16. Extremal problems
17. Matrix-valued holomorphic functions
18. Matrix equations
19. Realization theory
20. Eigenvalue location problems
21. Zero location problems
22. Convexity
23. Matrices with nonnegative entries
A. Some facts from analysis
B. More complex variables
Bibliography
Notation Index
Subject Index 

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Linear Algebra,Action 2nd Edition,Harry Dym