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020 _a9780387794280
_9978-0-387-79428-0
024 7 _a10.1007/978-0-387-79428-0
_2doi
040 _cCUS
050 4 _aQA251.3
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_2bicssc
072 7 _aMAT002010
_2bisacsh
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_2thema
082 0 4 _a512.44
_223
100 1 _aCarrell, James B.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGroups, Matrices, and Vector Spaces
_h[electronic resource] :
_bA Group Theoretic Approach to Linear Algebra /
_cby James B. Carrell.
250 _a1st ed. 2017.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2017.
300 _aXVII, 410 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _a1. 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.
520 _aThis 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.
650 0 _aCommutative algebra.
650 0 _aCommutative rings.
650 0 _aMatrix theory.
650 0 _aAlgebra.
650 0 _aGroup theory.
650 0 _aAlgebraic geometry.
650 1 4 _aCommutative Rings and Algebras.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11043
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11094
650 2 4 _aGroup Theory and Generalizations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11078
650 2 4 _aAlgebraic Geometry.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11019
856 4 0 _uhttps://doi.org/10.1007/978-0-387-79428-0
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