Drazin inverse of singular adjacency matrices of directed weighted cycles

• Andrés M. Encinas ^[1] ; Daniel A. Jaume ^[2] ; Cristian Panelo ^[2] ; Adrián Pastine ^[2]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  2. [2] Universidad Nacional de San Luis

     Universidad Nacional de San Luis

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 2, 2020, págs. 209-227
• Idioma: inglés
• DOI: 10.33044/revuma.v61n2a02
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• Resumen

  • 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.