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The converse of the Cowling–Obrechkoff–Thron theorem

Devon N. Munger and Pietro Paparella
Vol. 18 (2025), No. 3, 473–478
DOI: 10.2140/involve.2025.18.473
Abstract

Here we establish the converse of the Cowling–Obrechkoff–Thron theorem. In addition to its theoretical interest, the result fills a gap in the proof of Kellogg’s celebrated eigenvalue inequality for matrices whose principal minors are positive or nonnegative.

Keywords
eigenvalue inequality, location of zeros, $P$ matrix, $P_0$ matrix
Mathematical Subject Classification
Primary: 26C10, 30C15
Secondary: 15A42
Milestones
Received: 26 July 2023
Accepted: 17 December 2023
Published: 28 April 2025

Communicated by Chi-Kwong Li
Authors
Devon N. Munger
University of Washington Bothell
Bothell, WA
United States
Pietro Paparella
Division of Engineering and Mathematics
University of Washington Bothell
Bothell, WA
United States
© 2025 MSP (Mathematical Sciences Publishers).