On nonnegative sign equivalent and sign similar factorizations of matrices

Abstract

It is shown that every real n × n matrix is a product of at most two nonnegative sign
equivalent matrices, and every real n × n matrix, n ≥ 2, is a product of at most three nonnegative
sign similar matrices. Finally, it is proved that every real n×n matrix is a product of totally positive
sign equivalent matrices. However, the question of the minimal number of such factors is left open.