Characterizing the positive semidefiniteness of signed Laplacians via Effective Resistances

Wei Chen, Ji Liu, Yongxin Chen, Sei Zhen Khong, Dan Wang, Tamer Başar, Li Qiu, Karl H. Johansson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A symmetric signed Laplacian matrix uniquely defines a resistive electrical circuit, where the negative weights correspond to negative resistances. The positive semidefiniteness of signed Laplacian matrices is studied in this paper using the concept of effective resistance. We show that a signed Laplacian matrix is positive semidefinite with a simple zero eigenvalue if, and only if, the underlying graph is connected, and a suitably defined effective resistance matrix is positive definite.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages985-990
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

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