000 | 04209nam a22005055i 4500 | ||
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001 | 978-0-387-79428-0 | ||
003 | DE-He213 | ||
005 | 20200812131832.0 | ||
007 | cr nn 008mamaa | ||
008 | 170902s2017 xxu| s |||| 0|eng d | ||
020 |
_a9780387794280 _9978-0-387-79428-0 |
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024 | 7 |
_a10.1007/978-0-387-79428-0 _2doi |
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040 | _cCUS | ||
050 | 4 | _aQA251.3 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002010 _2bisacsh |
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072 | 7 |
_aPBF _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. |
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300 |
_aXVII, 410 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-SXMS | ||
942 | _cEBK | ||
999 |
_c206069 _d206069 |