Eigenvectors of Permutation Matrices
Affiliation(s)
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain.
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain.
ABSTRACT
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.
Cite this paper
Garca-Planas, M. and Magret, M. (2015) Eigenvectors of Permutation Matrices. Advances in Pure Mathematics, 5, 390-394. doi: 10.4236/apm.2015.57038.
Garca-Planas, M. and Magret, M. (2015) Eigenvectors of Permutation Matrices. Advances in Pure Mathematics, 5, 390-394. doi: 10.4236/apm.2015.57038.
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] Fripertinger, H. (2011) The Number of Invariant Subspaces under a Linear Operator on Finite Vector Spaces. Advances in Mathematics of Communications, 2, 407-416.
http://dx.doi.org/10.3934/amc.2011.5.407
[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] Fripertinger, H. (2011) The Number of Invariant Subspaces under a Linear Operator on Finite Vector Spaces. Advances in Mathematics of Communications, 2, 407-416.
http://dx.doi.org/10.3934/amc.2011.5.407