On the separation of eigenvalues by the permutation group
Grega Cigler ; Marjan Jerman
Special Matrices, Tome 2 (2014), p. 61-67 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267381 
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     author = {Grega Cigler and Marjan Jerman},
     title = {On the separation of eigenvalues by the permutation group},
     journal = {Special Matrices},
     volume = {2},
     year = {2014},
     pages = {61-67},
     zbl = {1291.15019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0006}
}

Grega Cigler; Marjan Jerman. On the separation of eigenvalues by the permutation group. Special Matrices, Tome 2 (2014) pp. 61-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0006/

[1] C. S. Ballantine, Stabilization by a diagonal matrix, Proc. Amer. Math. Soc. 25 (1970), 728-734. | Zbl 0228.15001

[2] G. Cigler, M. Jerman, On separation of eigenvalues by certain matrix subgroups, Linear Algebra Appl. 440 (2014), 213-217.[WoS] | Zbl 1286.15007

[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] | Zbl 1244.15006

[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] | Zbl 1232.15008

[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. | Zbl 0085.33102

[6] S. Friedland, On inverse multiplicative eigenvalue problems for matrices, Linear Algebra Appl. 12 (1975), 127-137. | Zbl 0329.15003

[7] H. Radjavi, P. Rosenthal, Simultaneous Triangularization, Universitext, Springer-Verlag, New York, 2000.