布尔矩阵的极小合g－逆和g－逆集的一个表示法

MINIMALg-INVERSES AND AN REPRESENTATION OFg-INVERSE SET FOR A BOOLEAN MATRIX

提出了布尔矩阵的极小ｇ－逆（广义逆）的概念，给出了求正则布尔矩阵的极小ｇ－逆集的一个算法和极小ｇ－逆个数的计算公式。根据ｇ－逆界定理，一个正则布尔矩阵Ａ的全部ｇ－逆可以通过Ａ的极小ｇ－逆集和最大ｇ－逆表示出来。

The concept of minimal generalized inverse(g-inverse)of a Boolean matrix ispresented in this paper.Then. an algorithm for finding all minimal g-inverses and a formulafor computing the number of minimal g- inverse of a regular square Boolean matrix are given. Hence. the g-inverse set of a regular matrix can be represented by its minimal inverse set andthe maximum g-inverse according to the g-inverse bounded theorem.