ON SOLUTIONS OF MATRIX EQUATION AXAT + BYBT = C

• 来源期刊: 计算数学(英文版)
• 关键词: Matrix equation Matrix norm QSVD Constrained condition Optimal problem.
• 年，卷（期）: 2005,（1）
• 页码范围: 17-26
• 页数: 10页
• 语种: 英文

摘要

By making use of the quotient singular value decomposition (QSVD) of a matrix pair,this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation AXAT + BYBT = C with the unknown X and Y, which may be both symmetric, skew-symmetric, nonnegative definite , positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.