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Groups, Matrices, and Vector Spaces [electronic resource] : A Group Theoretic Approach to Linear Algebra / by James B. Carrell.

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dc.contributor.author Carrell, James B. author.
dc.contributor.author SpringerLink (Online service)
dc.date.accessioned 2017-11-27T16:38:30Z
dc.date.available 2017-11-27T16:38:30Z
dc.date.created 2017.
dc.date.issued 2017
dc.identifier.isbn 9780387794280
dc.identifier.uri http://dspace.conacyt.gov.py/xmlui/handle/123456789/1840
dc.description XV, 410 p.
dc.description.abstract This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material.  Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.
dc.description.tableofcontents 1. Preliminaries -- 2. Groups and Fields: The Two Fundamental Notions of Algebra -- 3. Vector Spaces -- 4. Linear Mappings -- 5. Eigentheory -- 6. Unitary Diagonalization and Quadratic Forms -- 7. The Structure Theory of Linear Mappings -- 8. Theorems on Group Theory -- 9. Linear Algebraic Groups: An Introduction -- Bibliography -- Index.
dc.language eng
dc.publisher New York, NY : Springer New York : Imprint: Springer, 2017.
dc.relation.ispartofseries Springer eBooks
dc.relation.uri http://cicco.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-0-387-79428-0
dc.subject Mathematics.
dc.subject Algebraic geometry.
dc.subject Commutative algebra.
dc.subject Commutative rings.
dc.subject Group theory.
dc.subject Matrix theory.
dc.subject Algebra.
dc.subject Mathematics.
dc.subject Commutative Rings and Algebras.
dc.subject Linear and Multilinear Algebras, Matrix Theory.
dc.subject Group Theory and Generalizations.
dc.subject Algebraic Geometry.
dc.subject.ddc 512.44 23
dc.subject.lcc QA251.3
dc.subject.other Mathematics and Statistics (Springer-11649)
dc.title Groups, Matrices, and Vector Spaces [electronic resource] : A Group Theoretic Approach to Linear Algebra / by James B. Carrell.
dc.type text
dc.identifier.doi 10.1007/978-0-387-79428-0
dc.identifier.bib 978-0-387-79428-0
dc.format.rdamedia computer
dc.format.rdacarrier online resource
dc.format.rda text file PDF

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