Geometry of Linear Matrix Inequalities - Netzer, Tim;Plaumann, Daniel
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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.…mehr

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Produktbeschreibung
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.

Autorenporträt
Johanna Frischauf studierte Mathematik an der Universität Innsbruck und hat einen Master- sowie Lehramtsabschluss. Ihre Promotion in Mathematik schloss sie im Jahr 2023 in Innsbruck ab. Sie hat viel Erfahrung in der universitären Lehre, ganz besonders im Lehramtsstudiengang Mathematik. Tim Netzer ist Professor für angewandte Algebra an der Universität Innsbruck. Er unterrichtet seit Jahren Studierende im gesamten Bachelor- und Masterstudium der Mathematik und dem Lehramtsstudium.
Rezensionen
"This book is part of Birkhäuser 'Compact Textbooks in Mathematics' series, which aims for concise books that are tailored in size and scope to a single semester course at a late undergraduate or early graduate student level. This book fits that bill precisely. ... There are two appendices, one on real algebraic geometry and one on convexity, which provide background. With these, the book is in principle self-contained ." (Tamon Stephen, Mathematical Reviews, March, 2025)