Possible Numbers of the 0-1 Rectangular Matrices Whose Rank Is 1 or 2

摘要：

We have the possible numbers of ones in a 0-1 matrix with given rank in the generic case and in the symmetric case. There are some unexpected phenomena. The rank 2 symmetric case is subtle. On this basis,we carry out the promotion of literature, from the square matrix to a rectangular matrix 0,1m×x with rank for the number of 1 or 2.The main conclusions:(1) σ1(m,n) = (2m -1)(2n -1),(2) σ2(m,n)=4n-2n(n-1)Σm-1 k=1 Ckm (Σm-k l=1 C1 m-k)3 n-2n(n-1)(2 m -1)2.

关键词： 0-1 matriz rank number of ones Rectangular matrices

作者: Jia-pei Tang Bai-hong Zhang

作者单位: Command and Engineering of Chemical Defense Chinese Peoples Liberation Army, Beijing 102205, P.R.China

会议类型: 国际会议

会议名称: The Third International Workshop on Applied Matriz Theory(第三届国际矩阵分析与应用会议)

会议地点: 杭州

会议语种:英文

页码: 970-973

在线出版日期: 2009-07-09（万方平台首次上网日期，不代表论文的发表时间）