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.
References
[1]
Fossorier, M.P.C. (2004) Quasi-Cyclic Low-Density Parity-Check Codes from Circulant Permutation Matrices. IEEE Transactions on Information Theory, 50, 1788-1793.
http://dx.doi.org/10.1109/TIT.2004.831841
[2]
Marshall, A.W., Olkin, I. and Arnold, B.C. (2011) Doubly Stochastic Matrices. Inequalities: Theory of Majorization and Its Applications. Springer, New York.
http://dx.doi.org/10.1007/978-0-387-68276-1
[3]
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. http://dx.doi.org/10.1016/S0304-4149(00)00046-6
[4]
Skiena, S. (1990) The Cycle Structure of Permutations 1.2.4. In: Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Addison-Wesley, Reading, 20-24.
[5]
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