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.
