Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

ISBN-13: 9781470434557 / Angielski / Miękka / 2018 / 104 str.

J. William Helton;Igor Klep;Scott McCullough

Spis treści

• Introduction
• Dilations and Free Spectrahedral Inclusions
• Lifting and Averaging
• A Simplified Form for $\vartheta $
• $\vartheta$ is the Optimal Bound
• The Optimality Condition $\alpha =\beta $ in Terms of Beta Functions
• Rank versus Size for the Matrix Cube
• Free Spectrahedral Inclusion Generalities
• Reformulation of the Optimization Problem
• Simmons' Theorem for Half Integers
• Bounds on the Median and the Equipoint of the Beta Distribution
• Proof of Theorem 2.1
• Estimating $\vartheta (d)$ for Odd $d$.
• Dilations and Inclusions of Balls
• Probabilistic Theorems and Interpretations continued
• Bibliography
• Index.