- 期刊
0-1 Matrices and Their Complements with Given Rank
摘要
A 0-1 matrix is an integer matrix in which each entry is either 0 or 1. The complement matrix of a 0-1 matrix A is defined by J-A, where J is the matrix in which each entry is 1. Rank of a matrix is a fundamental concept in linear algebra, which measures the maximum number of linear independent rows or columns in a matrix. We give a complete characterization of those rectangular 0-1 matrices A for which the sum of the rank of A and the rank of J-A is 1, 2 and 3. The symmetric case can also be deduced.
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