期刊论文

中文

黑龙江大学自然科学学报

1001-7011

2004

21

4

79-84

10.3969/j.issn.1001-7011.2004.04.019

Supported by the Natural Science Foundation of China under （10171031 ; 50208004）；

本校为其他机构

设P为一给定的对称正交矩阵, 记AARP = {A ∈ Rn n ×n AT = ?A,（PA）T = ?PA}. 讨论下列问题:问题Ⅰ给定X,B ∈ Rn ×m . 求A ∈ AARP使 AX ? B = min. n问题Ⅱ设A? ∈ Rn , 求A? ∈ SE 使 A? ? A? = infA ×n ∈SE A? ? A , 其中SE为问题Ⅰ的解集合, · 表示Frobenius范数. 研究AARP中元素的通式, 给出问题Ⅰ解的一般表达式, 证明了问题Ⅱ存在唯一逼近解A?, 且 n得到了此解的具体表达式.

Given P ∈ Orn×n satisfying pT = p. A ∈ Rn×n is called anti-symmetric ortho-antisymmetric matrix if A = -AT, (PA)T = -PA. The set of all n × n anti-symmetric ortho-antisymmetric matrices is denoted by AARp. The following two problems are discussed in this paper:Problem Ⅰ: Given X, B ∈ Rn×m, find A ∈ AARnp such that f(A) = ‖AX - B‖ = min,Problem Ⅱ: Given A ∈ Rn×n, find A* ∈ SE such that ‖A~-A*‖=A∈SE‖A~-A‖ where ‖·‖ is the Frobenius norm, and SE is given. For Problem Ⅱ, the expression of the solution is provided. Futhermore...