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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Textbook 2023 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..

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2296-4568 oss diverse fieldsThis 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 gu

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Spectrahedral Shadows,ogramming, and in contrast to spectrahedra, many of the standard constructions from convexity theory can be applied to them. We explain how general semialgebraic sets can be approximated by spectrahedral shadows and how these methods provide criteria for being a spectrahedral shadow for many sets. W

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