The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.
 Fossorier, M.P.C. (2004) Quasi-Cyclic Low-Density Parity-Check Codes from Circulant Permutation Matrices. IEEE Transactions on Information Theory, 50, 1788-1793.
 Marshall, A.W., Olkin, I. and Arnold, B.C. (2011) Doubly Stochastic Matrices. Inequalities: Theory of Majorization and Its Applications. Springer, New York.
 Hamblya, B.M., Keevashc, P., O’Connella, N. and Starka, D. (2000) The Characteristic Polynomial of a Random Permutation Matrix. Stochastic Processes and Their Applications, 90, 335-346.
 Fripertinger, H. (2011) The Number of Invariant Subspaces under a Linear Operator on Finite Vector Spaces. Advances in Mathematics of Communications, 2, 407-416.