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。
<Abstrcat>This paper considers the following problem:Problem Ⅰ,given A∈R~^(n×m),D∈(R)^(m×m)such 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.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2005年第6期699-701,共3页
Journal of Hefei University of Technology：Natural Science
关键词
矩阵方程
反对称次对称矩阵
最小二乘解
标准相关分解
matrix equation
anti-symmetric and persymmetric matrix
least-square solution
canonical correlation decomposition
