On the separation of eigenvalues by the permutation group-Reference-Cited by-同舟云学术

On the separation of eigenvalues by the permutation group

Published:2014-01-01 Issue:1 Volume:2 Page:
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Cigler Grega¹,Jerman Marjan¹

Affiliation:

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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.2478/spma-2014-0006/pdf

Reference7 articles.

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

2. [2] G. Cigler, M. Jerman, On separation of eigenvalues by certain matrix subgroups, Linear Algebra Appl. 440 (2014), 213-217.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000329557700016&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3

3. [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.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000302852700065&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3

4. [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.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000297431200012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3

5. [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.

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