Systems of Linear Equations with Non-Negativity Constraints: Hyper-Rectangle Cover Theory and Its Applications

In this paper, a novel hyper-rectangle cover theory is developed. Two important concepts, the cover order and the cover length, are introduced. We construct a specific échelon form of the matrix in the same manner as that employed to determine the rank of the matrix to obtain the cover order of any given matrix. Using the properties of the cover order, we obtain the necessary and sufficient conditions for the existence and uniqueness of the …