北美最流行

高等线性代数

Nicholas Locher,"Advanced Linear Algebra"

2014 | ISBN: 1466559012 | 632 pages | PDF | 4,6 MB

【作者简介】

NICHOLAS LOEHR为美国Virginia Polytechnic Institute and State University数学系教授。

【教材简介】

Designedfor advanced undergraduate and beginning graduate students in linear orabstract algebra, Advanced Linear Algebra covers theoretical aspects of thesubject, along with examples, computations, and proofs. It explores a varietyof advanced topics in linear algebra that highlight the rich interconnectionsof the subject to geometry, algebra, analysis, combinatorics, numericalcomputation, and many other areas of mathematics.
The book’s 20 chapters are grouped into six mainareas: algebraic structures, matrices, structured matrices, geometric aspectsof linear algebra, modules, and multilinear algebra. The level of abstractiongradually increases as students proceed through the text, moving from matricesto vector spaces to modules.
Each chapter consists of a mathematical vignettedevoted to the development of one specific topic. Some chapters look atintroductory material from a sophisticated or abstract viewpoint while othersprovide elementary expositions of more theoretical concepts. Several chaptersoffer unusual perspectives or novel treatments of standard results. Unlikesimilar advanced mathematical texts, this one minimizes the dependence of eachchapter on material found in previous chapters so that students may immediatelyturn to the relevant chapter without first wading through pages of earliermaterial to access the necessary algebraic background and theorems.
Chapter summaries contain a structured list ofthe principal definitions and results. End-of-chapter exercises aid students indigesting the material. Students are encouraged to use a computer algebrasystem to help solve computationally intensive exercises.

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