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Titlebook: Computational Linear and Commutative Algebra; Martin Kreuzer,Lorenzo Robbiano Textbook 2016 Springer International Publishing Switzerland

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书目名称Computational Linear and Commutative Algebra
编辑Martin Kreuzer,Lorenzo Robbiano
视频videohttp://file.papertrans.cn/233/232583/232583.mp4
概述Most of the material is not yet available in book form.Combines linear and commutative algebra in a novel, unified way.Every chapter starts with a lively and humorous introduction to the topic.Follows
图书封面Titlebook: Computational Linear and Commutative Algebra;  Martin Kreuzer,Lorenzo Robbiano Textbook 2016 Springer International Publishing Switzerland
描述.This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the .Linear Algebra of the Third Millennium,. developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems.. .This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is notavailable at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations..
出版日期Textbook 2016
关键词commuting endomorphisms; generalized eigenspace; multiplication map; zero-dimensional affine algebra; pr
版次1
doihttps://doi.org/10.1007/978-3-319-43601-2
isbn_softcover978-3-319-82865-7
isbn_ebook978-3-319-43601-2
copyrightSpringer International Publishing Switzerland 2016
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Martin Kreuzer,Lorenzo RobbianoMost of the material is not yet available in book form.Combines linear and commutative algebra in a novel, unified way.Every chapter starts with a lively and humorous introduction to the topic.Follows
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https://doi.org/10.1007/978-3-8350-9596-0tive subalgebra of the ring of the .-endomorphisms of .. Given an ideal . in ℱ, the kernel of . is the intersection of the kernels of all endomorphisms in .. Now it turns out that the joint eigenspaces of ℱ are precisely the kernels of its maximal ideals, and . is the direct sum of the joint general
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https://doi.org/10.1007/978-3-8350-9596-0zero-dimensional affine algebra . over a field ., the multiplication endomorphisms define a commuting family ℱ, called the multiplication family. Via the natural isomorphism between . and ℱ, we get a number of interesting connections: the joint generalized eigenspaces of ℱ are the local factors of .
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