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

2012/10/21 by Matthew M. Lin, Lin, Matthew M., Chun-Yueh Chiang +1
Computer Science · Mathematics · #Matrix Theory and Algorithms #Algebraic and Geometric Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1210.5731

Abstract

We consider the \top-Stein equation X = AX^\top B + C, where the operator (⋅)^\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 X. In the second part, a numerical algorithm for solving \top-Stein equation is given under the solvability conditions.

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