Share This Article:

Eigenvectors of Permutation Matrices

Abstract Full-Text HTML XML Download Download as PDF (Size:213KB) PP. 390-394
DOI: 10.4236/apm.2015.57038    5,364 Downloads   6,013 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

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

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.