【摘要】 该文研究的问题为:给定A∈Rn×m,D∈Rm×m求X∈ASRn×n,使得‖ATXA-D‖F=min。这里ASRn×n表示全体n×n阶反对称次对称矩阵的集合,‖·‖表示Frobinius范数;利用矩阵对的标准相关分解(CCD),得到了该问题的通解表达式及矩阵方程ATXA=D有反对称次对称解的充分必要条件。更多还原

【Abstract】 <Abstrcat>This paper considers the following problem:Problem Ⅰ,given A∈R^<sup>n×m,D∈（R）^m×msuch that （Φ=‖A^TXA-D‖_F=min） where ASR^n×n is the set of real n-by-n anti-symmetric and persymmetric matrices, ‖·‖ is Frobenius norm.By applying the canonical decomposition （CCD） of matrix pairs,obtained herein are the general form of the solutions of Problem Ⅰ and necessary and sufficient conditions for the existence of the solutions of anti-symmetric and persymmetric matrices about the matrix equation A^TXA=D.更多还原