Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics.
The book's 20 chapters are grouped into six main areas: algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. The level of abstraction gradually increases as students proceed through the text, moving from matrices to vector spaces to modules.
Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. Unlike similar advanced mathematical texts, this one minimizes the dependence of each chapter on material found in previous chapters so that students may immediately turn to the relevant chapter without first wading through pages of earlier material to access the necessary algebraic background and theorems.
Chapter summaries contain a structured list of the principal definitions and results. End-of-chapter exercises aid students in digesting the material. Students are encouraged to use a computer algebra system to help solve computationally intensive exercises.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Postgraduate
Illustrationen
25 s/w Abbildungen
25 Illustrations, black and white
Maße
Höhe: 254 mm
Breite: 178 mm
Gewicht
ISBN-13
978-1-032-91809-9 (9781032918099)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Virginia Technical University, Blacksburg, USA
Background on Algebraic Structures. Overview of Algebraic Systems. Permutations. Polynomials. Matrices. Basic Matrix Operations. Determinants via Calculations. Concrete vs. Abstract Linear Algebra. Matrices with Special Structure. Hermitian, Positive Definite, Unitary, and Normal Matrices. Jordan Canonical Forms. Matrix Factorizations. Iterative Algorithms in Numerical Linear Algebra. The Interplay of Geometry and Linear Algebra. Affine Geometry and Convexity. Ruler and Compass Constructions. Dual Spaces and Bilinear Forms. Metric Spaces and Hilbert Spaces. Modules, Independence, and Classification Theorems. Finitely Generated Commutative Groups. Axiomatic Approach to Independence, Bases, and Dimension. Elements of Module Theory. Principal Ideal Domains, Modules over PID's, and Canonical Forms. Universal Mapping Properties and Multilinear Algebra. Introduction to Universal Mapping Properties. Universal Mapping Problems in Multilinear Algebra. Appendix: Basic Definitions. Sets. Functions. Relations. Partially Ordered Sets. Further Reading. Bibliography. Index.
