2019/04/08 by Enide Andrade, Andrade, Enide, Luis Arrieta +3
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1904.04172
openalex publication_date 2019/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A g-circulant matrix of order n is defined as a matrix of order n where each row is a right cyclic shift in g-places to the preceding row. Using number theory, certain nonnegative g-circulant real matrices are constructed. In particular, it is shown that spectra with sufficient conditions so that it can be the spectrum of a real g-circulant matrix is not a spectrum with sufficient conditions so that it can be the spectrum of a real circulant matrix of the same order. The obtained results are applied to Nonnegative Inverse Eigenvalue Problem to construct nonnegative, g-circulant matrices with given appropriated spectrum. Moreover, nonnegative g-circulant matrices by blocks are also studied and in this case, their orders can be a multiple of a prime number.