Synopses & Reviews
Review
The textbook can be used for a second course in linear algebra or asecond course in abstract algebra for advanced undergraduate or beginning graduate mathematics students. Loehr has minimized thedependence of each chapter on material found in earlier chapters, but notes that the level of abstraction gradually increasesthroughout. He covers the background on algebraic structures; matrices; matrices with special structure; the interplay of geometryand linear algebra; modules, independence, and classification theorems; and universal mapping properties and multilinear algebra.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Synopsis
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.
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