# On Theorems of Sinajova, Rankin and Kuperberg Concerning Spherical Point Configurations

## TL;DR

This paper provides straightforward linear algebraic proofs of theorems by Sinajova, Rankin, and Kuperberg on spherical point configurations, utilizing spherical Euclidean distance matrices and the Perron-Frobenius theorem.

## Contribution

It introduces simple linear algebraic proofs for existing theorems on spherical point configurations, highlighting a common approach using distance matrices and Perron-Frobenius theory.

## Key findings

- Unified proof technique for multiple theorems
- Application of Perron-Frobenius theorem in geometry
- Simplification of existing proofs

## Abstract

This note presents simple linear algebraic proofs of theorems due to Sinajova, Rankin and Kuperberg concerning spherical point configurations. The common ingredient in these proofs is the use of spherical Euclidean distance matrices and the Perron-Frobenius theorem.