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Linear Matrix Inequalities and Spectrahedra

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Geometry of Linear Matrix Inequalities

Part of the book series: Compact Textbooks in Mathematics ((CTM))

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Abstract

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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Notes

  1. 1.

    By the Nullstellensatz, this is equivalent to showing that the ideal generated by g and h is radical. This can be deduced from Bézout’s Theorem for curves, or directly from Max Noether’s AF + BG Theorem (see [29]).

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Authors and Affiliations

  1. Institut für Mathematik, Universität Innsbruck, Innsbruck, Austria

    Tim Netzer

  2. Fakultät für Mathematik, Technische Universität Dortmund, Dortmund, Nordrhein-Westfalen, Germany

    Daniel Plaumann

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  1. Tim Netzer
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  2. Daniel Plaumann
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Netzer, T., Plaumann, D. (2023). Linear Matrix Inequalities and Spectrahedra. In: Geometry of Linear Matrix Inequalities. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-26455-9_2

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