English

On the Sylvester matrix equation over quaternions

Rings and Algebras 2015-05-15 v1

Abstract

The Sylvester equation AXXB=CAX-XB=C is considered in the setting of quaternion matrices. Conditions that are necessary and sufficient for the existence of a unique solution are well-known. We study the complementary case where the equation either has infinitely many solutions or does not have solutions at all. Special attention is given to the case where AA and BB are respectively, lower and upper triangular two-diagonal matrices (in particular, if AA and BB are Jordan blocks)

Keywords

Cite

@article{arxiv.1505.03575,
  title  = {On the Sylvester matrix equation over quaternions},
  author = {Vladimir Bolotnikov},
  journal= {arXiv preprint arXiv:1505.03575},
  year   = {2015}
}
R2 v1 2026-06-22T09:33:54.249Z