Relationship between some Linear Matrix Functions

Abstract

n this work we focus on some linear matrix functions and their domains defined over the field of complex numbers ℂ, we discuss the intersections, the inclusion as well as the equality of two domains of some linear matrix functions, then by applying a specific matrix analytic tools on ranks and ranges, we consider certain forms of linear matrix equations, the general solutions to which can be expressed via specific explicit linear matrix functions to establish some relationships between its domains. As a consequence, we derive connections between some domains constrained by some matrix equations. Further, we characterize the relationship between generalized inverses of two matrices.