Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
 
Author index
To appear
 
Other MSP journals
Null vectors, Schur complements, and Parter vertices

Shaun Fallat and Johnna Parenteau

Vol. 15 (2022), No. 5, 843–856
Abstract

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.

Keywords
Schur complements, nullspace, Parter vertices, eigenvalues, multiplicity
Mathematical Subject Classification
Primary: 15A18
Secondary: 05C50
Milestones
Received: 12 November 2021
Accepted: 26 January 2022
Published: 3 March 2023

Communicated by Chi-Kwong Li
Authors
Shaun Fallat
Department of Mathematics and Statistics
University of Regina
SK
Canada
Johnna Parenteau
Department of Mathematics and Statistics
University of Regina
SK
Canada