In further pursuit of a solution to the celebrated nonnegative inverse eigenvalue problem, Loewy and London ((1978/1979) [8]) posed problem characterizing all polynomials that preserve matrices fixed order. If Pn denotes set n-by-n matrices, then it is clear with coefficients belong Pn. However, known contains negative entries. this work, novel results for respect belonging Along way, generaliz...

Using the relationship between totally nonnegative matrices and directed acyclic weighted planar networks, we show that 2× 2 minors of minor matrices of totally nonnegative matrices are also nonnegative. We give a combinatorial interpretation for the minors of minor matrices in terms of the weights of families of paths in a network. Introduction By attaching weights to the edges of a finite, di...