Complex and real counterexamples to an inequality arising from Drury's conjecture
Year: 2026
Type: preprint
Abstract: We give counterexamples to the following inequality, stated by Zhang as a consequence of Drury's 2016 permanent conjecture: if A = (ajk)j,k=1n is a Hermitian positive semidefinite matrix of order n ≥ 2, then ∑j=1n−1 |ajn|2 per A[ĵ, n̂] ≤ per A, where A[ĵ, n̂] is the principal submatrix obtained by deleting indices j and n. Our complex example has order twelve and rank two; our real example has order twenty-one and rank three.
Author: Lavi, Yair
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222901487
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