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

Matthew M. Lin; Chun-Yueh Chiang

paper

On the $⊤$ -Stein equation $X = A X^{⊤} B + C$

arXiv:1210.5731

Abstract

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

On the ⊤-Stein equation X=AX⊤B+C

Abstract

On the $⊤$ -Stein equation $X = A X^{⊤} B + C$