bibkey: bhatia2016mean
authors: R. Bhatia and T. Jain
year: 2016
title: "Mean matrices and conditional negativity"
doi: 10.13001/1081-3810.3082
url: https://journals.uwyo.edu/index.php/ela/article/view/1495
claim: "Section 2.9, Conjecture 1 asks for the class A range of Stolarsky mean matrices."
strata_touched:
  - D5/S3/Quantum/Matrix/StolarskyMean/Defs
  - D5/S3/Quantum/Matrix/StolarskyMean/KernelFactor
license: citation-only
triage: anchor

Stolarsky mean matrices

Locator

DOI supplied with the source: https://doi.org/10.13001/1081-3810.3082

Article: https://journals.uwyo.edu/index.php/ela/article/view/1495

R. Bhatia and T. Jain, Mean matrices and conditional negativity, Electronic Journal of Linear Algebra 29 (2016), 206–222, section 2.9. The DOI-to-PDF correspondence has not been independently verified in this offline implementation; no source PDF was available locally.

Source statement

This family does not yield readily to our analysis. We have some evidence for the following:

Conjecture 1. Let λ1, λ2, . . . , λn be positive numbers. The matrix [Sγ(λi, λj)] is in the class A if γ ≥ 2 but this is not always so when 0 ≤ γ < 2.

The source defines class A by positive entries and exactly one positive eigenvalue. The continuous Stolarsky extensions at equal inputs and at parameters zero and one are part of the intended mean definition. Theorems 2.10 and 2.11 supply the parameters three and four. The arithmetic parameter two is already covered by the earlier analysis.

Source boundary

The quotation, bibliographic data, theorem references, and literature status are supplied information. They do not constitute independent PDF verification or an exhaustive citation-index check. The formal definitions retain the real parameter and all positive finite node families, including repeated nodes.