Stephan Ramon Garcia

Second Course in Linear Algebra (eBook, PDF)

• Format: PDF

Produktbeschreibung

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).

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 11. Mai 2017
• Englisch
• ISBN-13: 9781108215909
• Artikelnr.: 48795768

Autorenporträt

Stephan Ramon Garcia is W. M. Keck Distinguished Service Professor and Professor of Mathematics at Pomona College, California. He is the author of two books and over seventy research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and other fields. He is on the editorial boards of the Proceedings of the American Mathematical Society, Involve, and the American Mathematical Monthly. He received three National Science Foundation (NSF) research grants as principal investigator, five teaching awards from three different institutions, and was twice nominated by Pomona College for the Council for Advancement and Support of Education (CASE) US Professors of the Year award.

Inhaltsangabe

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.

Rezensionen

'A Second Course in Linear Algebra by Garcia and Horn is a brilliant piece of work in linear algebra and matrix theory; it is a fascinating text for advanced undergraduate students and graduate students in science, technology, engineering and mathematics (STEM). Covering not only standard material but also many interesting topics, it presents the most fundamental and beautiful ideas in the field with cutting edge applications (such as the singular value decomposition with the Mona Lisa image). The book will become a standard text that is interesting and enjoyable for students as well as researchers.' Fuzhen Zhang, Nova Southeastern University, Florida