摘要
J.B.Kelly于1968年讨论了非负整数对称阵的可实现性问题,即:已知n阶非负整数对称阵B,问是否存在一个n×m的0-1矩阵A使得B=AA^T,并称满足条件的最小m为可实现矩阵B的容度.J.B. Kelly给出了n=1,2,3,4时矩阵B可实现的条件,并在B可实现时给出了它的容度.通过构造实现矩阵,很容易获得了n=1,2,3时相应的结论,并给出了3阶可实现矩阵B较为简便的容度算法.特别地,在B可实现时给出了其实现矩阵.
In 1968, J. B. Kelly investigated the realizability problem of nonnegative integral symmetric matrices, i. e. , under what conditions there exists an n × m 0-1 matrix A for a given n-order nonnegative integral symmetric matrix B such that B =AA^Y？ He defined the minimum m which meets the conditions above as the content of B. J. B. Kelly gave the realizable conditions for matrix B when n = 1,2,3,4 and its content. In this paper, we obtain the same results for n = 1,2,3 by directly constrcuting its realizable matrices, and give an easier algorithm of contents for 3-order realizable matrices. In particular, we give the realization matrix of B if it is realizable.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第2期146-151,共6页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(10671138)资助项目
关键词
非负整数对称矩阵
0-1矩阵
可实现矩阵
容度
Nonnegative integral symmetric matrix
Zero-one matrix
Realizable matrix
Content
