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A SECOND COURSE IN LINEAR ALGEBRA
Título:
A SECOND COURSE IN LINEAR ALGEBRA
Subtítulo:
Autor:
RAMON GARCIA, S
Editorial:
CAMBRIDGE UNIVERSITY PRESS
Año de edición:
2017
ISBN:
978-1-107-10381-8
Páginas:
2019
67,60 €

 

Sinopsis

Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. Concise chapters promote a focused progression through essential ideas, and contain many examples and illustrative graphics. In addition, each chapter contains a bullet list summarising important concepts, and the book includes over 600 exercises to aid the reader´s understanding. Topics are derived and discussed in detail, including the singular value decomposition, the Jordan canonical form, the spectral theorem, the QR factorization, normal matrices, Hermitian matrices (of interest to physics students), and positive definite matrices (of interest to statistics students).

Concise chapters focus on essential ideas
Special topics sections appeal to a broad range of disciplines
Numerous examples and over six hundred exercises prepare students for advanced topics and applications



Preliminaries
1. Vector spaces
2. Bases and similarity
3. Block matrices
4. Inner product spaces
5. Orthonormal vectors
6. Unitary matrices
7. Orthogonal complements and orthogonal projections
8. Eigenvalues, eigenvectors, and geometric multiplicity
9. The characteristic polynomial and algebraic multiplicity
10. Unitary triangularization and block diagonalization
11. Jordan canonical form
12. Normal matrices and the spectral theorem
13. Positive semidefinite matrices
14. The singular value and polar decompositions
15. Singular values and the spectral norm
16. Interlacing and inertia
Appendix A. Complex numbers.