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Über dieses Buch

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

Inhaltsverzeichnis

Frontmatter

2010 | OriginalPaper | Buchkapitel

Chapter 1. Elementary Linear and Multilinear Algebra

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 2. What Are Matrices

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 3. Square Matrices

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 4. Tensor and Exterior Products

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 5. Matrices with Real or Complex Entries

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 6. Hermitian Matrices

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 7. Norms

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 8. Nonnegative Matrices

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 9. Matrices with Entries in a Principal Ideal Domain; Jordan Reduction

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 10. Exponential of a Matrix, Polar Decomposition, and Classical Groups

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 11. Matrix Factorizations and Their Applications

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 12. Iterative Methods for Linear Systems

Denis Serre

2010 | OriginalPaper | Buchkapitel

Chapter 13. Approximation of Eigenvalues

Denis Serre

Backmatter

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