English

On the $\top$-Stein equation $X=AX^\top B+C$

Numerical Analysis 2012-10-23 v1

Abstract

We consider the \top-Stein equation X=AXB+CX = AX^\top B + C, where the operator ()(\cdot)^\top denotes the transpose (\top) of a matrix. In the first part of this paper, we analyze necessary and sufficient conditions for the existence and uniqueness of the solution XX. In the second part, a numerical algorithm for solving \top-Stein equation is given under the solvability conditions.

Keywords

Cite

@article{arxiv.1210.5731,
  title  = {On the $\top$-Stein equation $X=AX^\top B+C$},
  author = {Matthew M. Lin and Chun-Yueh Chiang},
  journal= {arXiv preprint arXiv:1210.5731},
  year   = {2012}
}