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Null vectors,
Schur complements, and Parter vertices
Shaun Fallat and Johnna Parenteau
Vol. 15 (2022), No. 5, 843–856
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Abstract |
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One of the most important historical contributions to the inverse eigenvalue problem associated with trees is the celebrated Parter–Wiener theorem. We offer an alternate elementary proof of this seminal result, utilizing the basic matrix tool known as the Schur-complement of a matrix, in connection with analyzing the nullspace structure of matrices whose graph is a tree. |
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Keywords
Schur complements, nullspace, Parter vertices, eigenvalues,
multiplicity
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Mathematical Subject Classification
Primary: 15A18
Secondary: 05C50
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Milestones
Received: 12 November 2021
Accepted: 26 January 2022
Published: 3 March 2023
Communicated by Chi-Kwong Li
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Authors |
| Shaun Fallat | |
| Department of Mathematics and
Statistics University of Regina SK Canada |
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| Johnna Parenteau | |
| Department of Mathematics and
Statistics University of Regina SK Canada |
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