Abstract
We consider square matrices arising as the sum of left and right circulant matrices and derive asymptotics of the sequence of their powers. Particular emphasis is laid on the case where the matrix has consecutive integer entries; we find explicit formulae for the eigenvalues and eigenvectors of the matrix in this case and find its Moore-Penrose pseudoinverse. The calculation involves the discrete Fourier transform of integer vectors arising from sum systems and exhibits a resonance phenomenon.
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