摘要
本文利用我在“逻辑关系方程的一种解法和有解条件”一文中所给出的逻辑关系方程的解法,讨论形式为A▽(x_1 x_2…x_n)=(0…0—0…0)(i)… (1)这样一类逻辑关系方程的解与布尔系数矩阵A之间的某些关系,并利用所得的结论,给出一种新证法证明了一个n×n的布尔矩阵A可逆的充分必要条件为A是置换矩阵,且A^(-1)=A^T.
In this paper, using the algorithm given in that paper, we shall discuss some relations between solutions for logical relation equations of the form and boolean matrix A.A new method is given to prove that a n×n boolean matrix A has inverse if and only if A is a permutation matrix, and showed that the inverse of a permutation matrix A is A^T.
出处
《辽宁大学学报（自然科学版）》
CAS
1989年第3期58-59,共2页
Journal of Liaoning University：Natural Sciences Edition
关键词
逻辑关系方程
布尔矩阵
置换矩阵
logical relation eguations
boolean matrices
permutation matrix
