Drazin inverse of singular adjacency matrices of directed weighted cycles

Authors

  • Andrés M. Encinas Departament de Matem`atiques. Universitat Polit`ecnica de Catalunya. Barcelona, Spain
  • Daniel Alejandro Jaume Departamento de Matemáticas. Facultad de Ciencias Fíısico-Matemáticas y Naturales.Universidad Nacional de San Luis. Instituto de Matemáticas Aplicadas de San Luis, IMASL–CONICET, San Luis, Argentina
  • Cristian Panelo Departamento de Matemáticas. Facultad de Ciencias Físico-Matemáticas y Naturales. Universidad Nacional de San Luis. San Luis, Argentina
  • Adrián Pastine Departamento de Matemáticas. Facultad de Ciencias Físico-Matemáticas y Naturales. Universidad Nacional de San Luis. Instituto de Matemáticas Aplicadas de San Luis, IMASL–CONICET, San Luis, Argentina

DOI:

https://doi.org/10.33044/revuma.v61n2a02

Abstract

 We present a necessary and sufficient condition for the singularity of circulant matrices associated with directed weighted cycles. This condition is simple and independent of the order of matrices from a complexity point of view. We give explicit and simple formulas for the Drazin inverse of these circulant matrices. We also provide a Bjerhammar-type condition for the Drazin inverse.

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Published

2020-09-25

Issue

Vol. 61 No. 2 (2020)

Section

Article

License

Copyright (c) 2024 Daniel Alejandro Jaume, Adrian Pastine, Dr., Andres M Encinas, Dr., Cristian Panelo, Prof.

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