【摘要】 <正> §1.问题的提出 R^n×m表示所有n×m阶实对称阵集合,Rⁿ=R^n×1,R_r^n×m表示R^n×m中秩为r的子集,Oⁿ是n阶正交阵之集,Sⁿ表示n阶实对称阵的全体,A⁺表示A的Moore-Penrose广义逆,I_k表示k阶单位阵,S_k=(e_k,e_k-1,…,e₁)∈R^k×k,其中e_i为单位阵I_k的第i列。R（A）表示A的列空间,N（A）表示A的零空间,rank（A）表示A的更多还原

【Abstract】 In this paper, we are concerned with the following two problems: Problem 1 we describe the set ASnE of real n -by-n anti-symmetric and persymmetric matrices such that minimize the Frobenius norm of AX - B for X, B in Rnxn; Problem 2 find the unique A in the set ASnE, satisfying ||A*- A|| - min ||A* - A||,where A* ∈ Rnxn is a given matrix, || ·|| is the Frobenius norm. We derive a general expression of the set ASnE. For Problem 2, we prove the existence and the uniqueness of the solution and provide the expression of this unique solution. We also report some numerical results to support the theory established in the paper.更多还原