The eigenvectors-eigenvalues identity and Sun's conjectures on determinants and permanents

TL;DR

This paper proves a conjecture by Sun from 2018 using the eigenvectors-eigenvalues identity discovered in 2019, linking eigenvalue techniques to properties of determinants and permanents.

Contribution

It establishes a new proof of Sun's conjecture by applying the eigenvectors-eigenvalues identity, bridging spectral methods with combinatorial matrix properties.

Findings

Confirmed Sun's conjecture on determinants and permanents

Demonstrated the utility of the eigenvectors-eigenvalues identity in combinatorial matrix theory

Provided a novel proof technique for conjectures in algebraic combinatorics

Abstract

In this paper, we prove a conjecture raised by Zhi-Wei Sun in 2018 by the eigenvectors-eigenvalues identity found by Denton, Parke, Tao and X. Zhang in 2019.