ELA, Volume 16, pp. 162-170, July 2007, abstract.

On Nonnegative Sign Equivalent and Sign Similar 
Factorizations of Matrices

Daniel Hershkowitz and Allan Pinkus

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