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Titlebook: Geometry of Linear Matrix Inequalities; A Course in Convexit Tim Netzer,Daniel Plaumann Textbook 2023 The Editor(s) (if applicable) and The

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发表于 2025-3-21 20:09:58 | 显示全部楼层 |阅读模式
书目名称Geometry of Linear Matrix Inequalities
副标题A Course in Convexit
编辑Tim Netzer,Daniel Plaumann
视频video
概述Unifies recent key results, along with elementary proofs.Includes many exercises for active learning.Appeals to mathematical researchers across diverse fields
丛书名称Compact Textbooks in Mathematics
图书封面Titlebook: Geometry of Linear Matrix Inequalities; A Course in Convexit Tim Netzer,Daniel Plaumann Textbook 2023 The Editor(s) (if applicable) and The
描述This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry..
出版日期Textbook 2023
关键词Real Algebraic Geometry; Convex Geometry; Matrices; Polynomial Optimization; Sums of Squares; Eigenvalues
版次1
doihttps://doi.org/10.1007/978-3-031-26455-9
isbn_softcover978-3-031-26454-2
isbn_ebook978-3-031-26455-9Series ISSN 2296-4568 Series E-ISSN 2296-455X
issn_series 2296-4568
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Das Konzept der zweiseitigen MärkteIn this first chapter we give an introduction and outline of the topics from the book. We also introduce basic notions and results from linear algebra, convexity theory and real algebraic geometry.
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Linear Matrix Inequalities and Spectrahedra,In this chapter we introduce the notion of a spectrahedron, and thoroughly study its properties. We will see many examples, and learn methods to determine whether a given set is a spectrahedron or not. In most cases we will also obtain procedures to explicitly construct defining linear matrix inequalities.
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https://doi.org/10.1007/978-3-031-26455-9Real Algebraic Geometry; Convex Geometry; Matrices; Polynomial Optimization; Sums of Squares; Eigenvalues
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Textbook 2023nomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general result
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