2026/08/03 by Vatsalkumar N. Mer
Mathematics · #math.RA #msc:15A86 #msc:15B48
arxiv created 2026/08/03 · arxiv updated 2026/08/04
An m-by-n real matrix A is said to be semipositive if there exists a vector x>0 such that Ax>0, where the inequalities are understood componentwise. Dorsey et al. conjectured that any invertible linear map that L that leaves invariant the collection of all semipositive matrices is always in the standard form A ↦ XAY for some row positive matrix X and inverse nonnegative matrix Y. This was settled in when m ≥ n. Our aim in this paper is to settle the case when m<n of the above conjecture. In fact, our proof works for arbitrary positive integers m and n. The main ingredient is a classification of affine subspaces of the largest possible dimension contained in the set of semipositive matrices.