The Linear Algebra a Beginning Graduate Student Ought to Know
Seiten
2004
Springer-Verlag New York Inc.
978-1-4020-1824-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4020-1824-4 (ISBN)
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Linear algebra is a living, active branch of mathematics. This book deals with the abstract theory and devotes considerable space to the numerical and computational aspects of linear algebra. It contains a number of thumbnail portraits of researchers who have contributed to the development of linear algebra.
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: as a self-study guide; as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or, as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: as a self-study guide; as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or, as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.
1. Notation and terminology.- 2. Fields.- 3. Vector spaces over a field.- 4. Algebras over a field.- 5. Linear Dependence and Dimension.- 6. Linear Transformations.- 7. The endomorphism algebra of a vector space.- 8. Representation of linear transformations by matrices.- 9. The algebra of square matrices.- 10. Systems of linear equations.- 11.Determinants.- 12. Eigenvalues and eigenvectors.- 13. Krylov subspaces.- 14. The dual space.- 15. Inner product spaces.- 16. Orthogonality.- 17. Selfadjoint endomorphisms.- 18. Unitary and normal endomorphisms.- 19. Moore-Penrose pseudoinverses.- 20. Bilinear transformations and forms.
| Erscheint lt. Verlag | 31.1.2004 |
|---|---|
| Reihe/Serie | Texts in the Mathematical Sciences ; v. 27 |
| Zusatzinfo | 1 |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 160 x 240 mm |
| Gewicht | 899 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-4020-1824-X / 140201824X |
| ISBN-13 | 978-1-4020-1824-4 / 9781402018244 |
| Zustand | Neuware |
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