M{2,3},M{2,4}和M{2,3,4}的有效刻画（英文）

Efficient characterization for M{2,3},M{2,4} and M{2,3,4}

集合A到集合B上的一个一一映射f称为B的一个有效刻画。本文提出的选逆象指标法(SIIIM)给出集A_1={α:α=(I_s,η)~T∈C_s^(n×s)}到象集B_1={β:β=α(α~*α)^(-1)α~*,α∈A_1}的一个有效刻画公式,并证明了B_1是I{2,3}_s的稠密子集,且I{2,3}_s的每个元素都与B_1的某个元素置换相似,利用上述结果,分别建立了I{2,3}和长方阵广义逆矩阵类M{2,3}.的有效刻画公式。再利用等式I{2,3}_s=I{2,4}_s=I{2,3,4}_s,进一步获得了M{2,4},M{2,3,4}的有效刻画公式.算法3.1可用于无重复地计算I{2,3}_s的任一个元素.

In this paper, by selecting inverse image index method, an efficient charac- terization formula from set A1={α：α=（Is,η）^T∈Cs^n×s） onto set B1={β：β=α（α^＊α）^-1α^＊,a∈A1} is given. Besides, it is shown that each element of I{2, 3}s is permutation similar to an element of B1. Then efficient characterization formulas for I{2, 3} and M{2, 3} are obtained respectively. An interesting thing is B1 is a dense subset of 1{2, 3}s. The fact that I{2, 3}s = I（2, 4）s = I（2, 3, 4}s enables us to obtain the efficient characterization formulas for M{2, 4} and M（2, 3, 4} fluently. Algorithm 3.1 may be used to compute elements of I{2, 3}s and to avoid the repeated computation work.