# On separation of eigenvalues by the permutation group

Special Matrices (2014)

- Volume: 2, Issue: 1, page 78-84
- ISSN: 2300-7451

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topGrega Cigler, and Marjan Jerman. "On separation of eigenvalues by the permutation group." Special Matrices 2.1 (2014): 78-84. <http://eudml.org/doc/266677>.

@article{GregaCigler2014,

abstract = {Let A be an invertible 3 × 3 complex matrix. It is shown that there is a 3 × 3 permutation matrix P such that the product PA has at least two distinct eigenvalues. The nilpotent complex n × n matrices A for which the products PA with all symmetric matrices P have a single spectrum are determined. It is shown that for a n × n complex matrix [...] there exists a permutation matrix P such that the product PA has at least two distinct eigenvalues.},

author = {Grega Cigler, Marjan Jerman},

journal = {Special Matrices},

keywords = {distinct eigenvalues; irreducible group; symmetric group},

language = {eng},

number = {1},

pages = {78-84},

title = {On separation of eigenvalues by the permutation group},

url = {http://eudml.org/doc/266677},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Grega Cigler

AU - Marjan Jerman

TI - On separation of eigenvalues by the permutation group

JO - Special Matrices

PY - 2014

VL - 2

IS - 1

SP - 78

EP - 84

AB - Let A be an invertible 3 × 3 complex matrix. It is shown that there is a 3 × 3 permutation matrix P such that the product PA has at least two distinct eigenvalues. The nilpotent complex n × n matrices A for which the products PA with all symmetric matrices P have a single spectrum are determined. It is shown that for a n × n complex matrix [...] there exists a permutation matrix P such that the product PA has at least two distinct eigenvalues.

LA - eng

KW - distinct eigenvalues; irreducible group; symmetric group

UR - http://eudml.org/doc/266677

ER -

## References

top- [1] C. S. Ballantine, Stabilization by a diagonal matrix, Proc. Amer. Math. Soc. 25 (1970), 728-34. Zbl0228.15001
- [2] G. Cigler, M. Jerman, On separation of eigenvalues by certain matrix subgroups, Linear Algebra Appl. 440 (2014), 213-217.[WoS] Zbl1286.15007
- [3] M. Choi, Z. Huang, C. Li, N. Sze, Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues, Linear Algebra Appl. 436 (2012), 3773-3776.[WoS] Zbl1244.15006
- [4] X. Feng, Z. Li, T. Huang, Is every nonsingular matrix diagonally equivalent to a matrix with all distinct eigenvalues?, Linear Algebra Appl. 436 (2012), 120-125.[WoS] Zbl1232.15008
- [5] M. E. Fisher, A. T. Fuller, On the stabilization of matrices and the convergence of linear iterative processes, Proc. Cambridge Philos. Soc. 54 (1958), 417-425. Zbl0085.33102
- [6] S. Friedland, On inverse multiplicative eigenvalue problems for matrices, Linear Algebra Appl. 12 (1975), 127-137. Zbl0329.15003
- [7] H. Radjavi, P. Rosenthal, Simultaneous Triangularization, Universitext, Springer-Verlag, New York, 2000.

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