摘要
本文证明了,对每个酉不变范数‖·‖_(UI)当x=A^(1,3)B时,‖AX-B‖_(UI)达到最小值;反之,如果Y具有这一性质:对每个酉不变范数‖·‖_(UI)以及任意矩阵B,当X=YB时,‖AX-B‖_(UI)达到最小值,则Y∈A{1,3}.还证明了A^+B是矩阵方程AX=B在每个酉不变范数之下的最佳逼近解,同时得出了X=A^+DB^+是矩阵方程AXB=D在每个酉不变范数之下的逼近解的条件。
In this paper, following conclusions are proved. For every unitarily invariant norm ‖·‖_(UI). ‖AX-B‖_(UI)is smallest when X=A^(1, 3)B. Converscly, if Y has the property, that for every unitarily invariant norm ‖·‖_(UI) and any B, ‖AX-B‖_(UI)is smallest when X=YB, then Y∈A{1, 3}. Moreover, A^+B is the best approximate solution of the matrix equation AX=B for every unitarily invariant norm. Finally, if some condition is satisfied, then X=A^+ DB^+ is an approximate solution of the matrix equation AXB=D for every unitarily invariant norm, but it is not a such solution in general.
出处
《南京师大学报（自然科学版）》
CAS
CSCD
1990年第4期1-6,14,共7页
Journal of Nanjing Normal University(Natural Science Edition)
关键词
广义
逆矩阵
酉不变范数
逼近解
Generalized inverses of matrices, Unitarily invariant norm, Symmetric gauge function, Best approximate solution.
