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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Das Konzept der zweiseitigen M?rkteIn 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