
Advanced Linear Algebra
Nicholas A. Loehr(Author)
CRC Press
1st Edition
Published on 10. April 2014
Book
Hardback
632 pages
978-1-4665-5901-1 (ISBN)
Article exhausted; check for reprint
Description
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.
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.
More details
Series
Language
English
Place of publication
Bosa Roca
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Product notice
sewn/stitched
Cloth over boards
Illustrations
25 s/w Abbildungen, 15 s/w Tabellen
15 Tables, black and white; 25 Illustrations, black and white
Dimensions
Height: 261 mm
Width: 184 mm
Thickness: 38 mm
Weight
1230 gr
ISBN-13
978-1-4665-5901-1 (9781466559011)
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Nicholas A. Loehr
Advanced Linear Algebra
Book
06/2024
2nd Edition
Chapman & Hall/CRC
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Nicholas A. Loehr
Advanced Linear Algebra
Book
10/2024
1st Edition
Chapman & Hall/CRC
€90.55
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Person
Nicholas Loehr
Content
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.