【摘要】 设S是实数集R的一个非空子集,如果存在S上的矩阵B,使得A=BBT,则称A是可S-因子分解的.对于一个实对称矩阵A,如果存在一个最小正整数k以及实矩阵(长方形)V,使得A=VVT,且V的每一列至多只有k个非零元素,则称A的因子宽度为k.利用可S-因子分解矩阵的S-秩以及因子宽度,引入相对因子宽度的定义,给出了一些可{0,1}-因子分解矩阵的相对因子宽度与因子分解之间的关系,最后利用S-秩和相对因子宽度,刻画了一类矩阵.更多还原

【Abstract】 Let S be a non-void subset of a set of real numbers R.A is called S-factorizable if it can be factorized as A=BBT with bij∈S.For a real symmetric matrix A,if there exists a minimum positive integer k and a real rectangular matrix V with A=VVT, and there are at most k non-zero elements in each column,the factor width of A is k.By use of S-rank and factor width of the S-factorizable matrix A,the concept of relative factor width was introduced, and the relationship between the relative factor width and factorization of some｛0,1｝-factorizable matrices was given.Finally,some matrices were characterized with S-rank and relative factor width.更多还原