• Corpus ID: 244773134

# Positive definite functions of noncommuting contractions, Hua-Bellman matrices, and a new distance metric

@inproceedings{Sra2021PositiveDF,
title={Positive definite functions of noncommuting contractions, Hua-Bellman matrices, and a new distance metric},
author={Suvrit Sra},
year={2021}
}
• S. Sra
• Published 30 November 2021
• Mathematics
We study positive definite functions on noncommuting strict contractions. In particular, we study functions that induce positive definite Hua-Bellman matrices (i.e., matrices of the form [det(I − Ai Aj)−α]ij where Ai and Aj are strict contractions and α ∈ C). We start by revisiting a 1959 work of Bellman (R. Bellman Representation theorems and inequalities for Hermitian matrices; Duke Mathematical J., 26(3), 1959) that studies Hua-Bellman matrices and claims a strengthening of Hua’s…

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