{"id":"hexagon/2610.00620","pdf":"https://hexagonmath.org/pdf/2610.00620v1","url":"https://hexagonmath.org/abs/2610.00620v1","tags":["math.OA","math.MG","msc:42A82","msc:47A63","msc:15B48","msc:46L53","msc:54E35","Hua-Bellman matrices","distance metric","noncommuting contractions"],"score":0,"title":"Positive definite functions of noncommuting contractions, Hua-Bellman matrices, and a new distance metric","domain":"math.FA","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.FA","summary":"We study positive definiteness of Hua-Bellman matrices (i.e., matrices of the form $[\\det(I-A_i^*A_j)^{-α}]_{ij}$, where $A_i$ and $A_j$ are strict contractions and $α\\in\\mathbb{R}$). We start by revisiting a 1959 work of Bellman (Representation theorems and inequalities for Hermitian matrices; Duke Mathematical J., 26(3), 1959) that studies positive definiteness of Hua-Bellman matrices and claims a strengthening of Hua's representation-theoretic results (Inequalities involving determinants; Acta Mathematica Sinica, 5 (1955)). We uncover a critical error in Bellman's proof that has…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}