Revista de la
Unión Matemática Argentina
Drazin inverse of singular adjacency matrices of directed weighted cycles
Andrés M. Encinas, Daniel A. Jaume, Cristian Panelo, and Adrián Pastine
Volume 61, no. 2 (2020), pp. 209–227

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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.