On the Yang-Baxter-like matrix equation for rank-two matrices

Duanmei Zhou; Guoliang Chen; Jiu Ding

Open Mathematics (2017)

  • Volume: 15, Issue: 1, page 340-353
  • ISSN: 2391-5455

Abstract

top
Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.

How to cite

top

Duanmei Zhou, Guoliang Chen, and Jiu Ding. "On the Yang-Baxter-like matrix equation for rank-two matrices." Open Mathematics 15.1 (2017): 340-353. <http://eudml.org/doc/288077>.

@article{DuanmeiZhou2017,
abstract = {Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.},
author = {Duanmei Zhou, Guoliang Chen, Jiu Ding},
journal = {Open Mathematics},
keywords = {Rank-two matrix; Matrix equation; Jordan form; rank-two matrix; quadratic matrix equation},
language = {eng},
number = {1},
pages = {340-353},
title = {On the Yang-Baxter-like matrix equation for rank-two matrices},
url = {http://eudml.org/doc/288077},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Duanmei Zhou
AU - Guoliang Chen
AU - Jiu Ding
TI - On the Yang-Baxter-like matrix equation for rank-two matrices
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 340
EP - 353
AB - Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
LA - eng
KW - Rank-two matrix; Matrix equation; Jordan form; rank-two matrix; quadratic matrix equation
UR - http://eudml.org/doc/288077
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.