On the separation of eigenvalues by the permutation group

• Autorzy: Grega Cigler , Marjan Jerman
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

distinct eigenvalues; irreducible group; symmetric group

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2014
• Tom: 2
• Numer: 1
• Strony: 61-67

Daty

wydano

2014-01-01

otrzymano

2013-12-19

zaakceptowano

2014-04-13

online

2014-05-17

Twórcy

autor

Grega Cigler

• Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

autor

Marjan Jerman

• Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Bibliografia

• [1] C. S. Ballantine, Stabilization by a diagonal matrix, Proc. Amer. Math. Soc. 25 (1970), 728-734.
• [2] G. Cigler, M. Jerman, On separation of eigenvalues by certain matrix subgroups, Linear Algebra Appl. 440 (2014), 213-217.[WoS]
• [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]
• [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]
• [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.
• [6] S. Friedland, On inverse multiplicative eigenvalue problems for matrices, Linear Algebra Appl. 12 (1975), 127-137.
• [7] H. Radjavi, P. Rosenthal, Simultaneous Triangularization, Universitext, Springer-Verlag, New York, 2000.

Identyfikatory

DOI

10.2478/spma-2014-0006