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The converse of
the Cowling–Obrechkoff–Thron theorem
Devon N. Munger and Pietro Paparella |
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Vol. 18 (2025), No. 3, 473–478
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Abstract |
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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. |
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Keywords
eigenvalue inequality, location of zeros, $P$ matrix, $P_0$
matrix
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Mathematical Subject Classification
Primary: 26C10, 30C15
Secondary: 15A42
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Milestones
Received: 26 July 2023
Accepted: 17 December 2023
Published: 28 April 2025
Communicated by Chi-Kwong Li
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Authors |
| Devon N. Munger | |
| University of Washington
Bothell Bothell, WA United States |
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| Pietro Paparella | |
| Division of Engineering and
Mathematics University of Washington Bothell Bothell, WA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
