I{2}和M{2}的有效刻画(英文)  

Efficient characterization for I{2} and M{2}

作　　者：征道生[1] 

机构地区：[1]华东师范大学数学系,上海200241

出　　处：《华东师范大学学报（自然科学版）》2015年第1期42-50,67,共10页Journal of East China Normal University(Natural Science)

摘　　要：Stewart给出了一个矩阵2-逆集合M{2}的刻画公式.但其中含有多余的任意参数,因而不是一个有效刻画.本文利用方阵的满秩分解,为I{2}_s的一个真子集B_1剔除了Stewart公式中的多余任意参数,得到了B_1的有效刻画公式;还证明了I{2}是其有限个子集的并集,其中每个子集与B_1等距同构.由此可分别建立I{2},I{2},M{2}和M{2}的有效刻画公式.算法2.1则可用于无重复地计算I{2}_s的每个元素.An important characterization formula for M{2} was given by Stewart where M ∈ Cm×n.But this formula contains redundant arbitrary parameters,and therefore is nonefficient.This paper,by using the matrix full rank decomposition,showed that for a proper subset of I{2}s,which is denoted as B1,the redundant arbitrary parameters in Stewart＇s formula can be eliminated,and I{2}s is a union set of its certain subsets,and each of the subsets is 2-norm isometry with B1.Finally,the efficient characterization fonmulas for I{2}s,I{2} and M{2} are obtained respectively.An algorithm was provided that can be used to compute any element of I{2}s,and avoid the repeat computation work for each element of I{2}s.

关 键 词：广义逆矩阵类的有效刻画 两个集合的2-范等距同构 矩阵的满秩分解 矩阵方程的解 

分 类 号：O151.21[理学—数学] O177.7[理学—基础数学]