On matrices which have signed null-spaces
Si-Ju Kim, Bryan L. Shader · Linear Algebra and its Applications · 2002
We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of A is S, for each A∈Q(A). We show that if A is an m by n matrix with no duplicate columns up to multiplication by −1 and A has signed null-space, then n⩽3m−2. We also classify the set of matrices satisfying the equality.