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Matrix Completions, Moments, and Sums of Hermitian Squares$
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Mihály Bakonyi and Hugo J. Woerdeman

Print publication date: 2011

Print ISBN-13: 9780691128894

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691128894.001.0001

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Cones of Hermitian matrices and trigonometric polynomials

Cones of Hermitian matrices and trigonometric polynomials

(p.1) Chapter One Cones of Hermitian matrices and trigonometric polynomials
Matrix Completions, Moments, and Sums of Hermitian Squares

Mihály Bakonyi

Hugo J. Woerdeman

Princeton University Press

This chapter studies cones in the real Hilbert spaces of Hermitian matrices and real valued trigonometric polynomials. Based on an approach using such cones and their duals, it establishes various extension results for positive semidefinite matrices and nonnegative trigonometric polynomials. In addition, it shows the connection with semidefinite programming and includes some numerical experiments. The discussions cover cones and their basic properties, cones of Hermitian matrices, cones of trigonometric polynomials, determinant and entropy maximization, and semidefinite programming. Exercises and notes are provided at the end of the chapter.

Keywords:   Hilbert spaces, Hermitian matrices, trigonometric polynomials, cones, semidefinite matrices, semidefinite programming

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