Characterizations Of Matrices With Nonnegative Core Inverses And Nonnegative Core-EP Inverses

Monotonic matrices not only have important theoretical significance and interest in nonnegative matrix theory,but also have important applications in many applied fields.Due to the importance of monotonic matrices,a natural problem is how to determine whether a matrix is monotonic or not,that is,how to characterize the structure of monotonic matrices.An important feature of monotonic matrices is nonsingularity,and singular matrices may occur in practical application problems,so it is necessary to generalize monotonic matrices from nonsingular matrices to singular matrices,at which the generalized inverses of matrices will be involved,that is,the problem of studying when nonnegative matrices have nonnegative generalized inverses.Characterizations for the nonnegativity of core inverses of nonnegative matrices are studied.A sufficient and necessary condition for core-monotonicity of nonnegative matrices is presented by nonnegative full-rank decomposition,the representation of the core inverse is also given when it is nonnegative.It is shown by some numerical examples that the nonnegativity of the core inverse and the Moore-Penrose,group inverse of nonnegative matrices are not equivalent.Furthermore,a sufficient and necessary condition for the core-monotonicity of real matrices is presented.A square matrix is said to have property n if there exists a positive integer w such that Aw is nonnegative.In this paper,we study the core-EP-monotonicity for property-n matrices.Some necessary and sufficient conditions for a property-n matrix to be core-EP-monotone are given.Moreover,a necessary and sufficient condition for a real square matrix to have a nonnegative core-EP inverse is also presented...