Linear operators which preserve sign-nonsingular matrices (Q1805301)

The authors characterize the linear operators \(T\) on the set of all \(n \times n\) real matrices that preserve the set \(N_ n\) of sign- nonsingular matrices. For \(n \geq 3\), they show that if \(T\) preserves \(N_ n\) then \(T\) also preserves the set of matrices of term rank 1. Their characterization is then obtained by using a result due to the first author and \textit{N. J. Pullman} [Proc. R. Ir. Acad., Sect. A 91, No. 1, 71-78 (1991; Zbl 0787.15003)].