Almost strictly totally negative matrices: An algorithmic characterization

A real matrix A=(aij)1≤i,j,≤nA=(aij)1≤i,j,≤n is said to be almost strictly totally negative if it is almost strictly sign regular with signature ε=(−1,−1,…,−1)ε=(−1,−1,…,−1), which is equivalent to the property that all its nontrivial minors are negative. In this paper an algorithmic characterization of nonsingular almost strictly totally negative matrices is presented.