TITLE:
EPr Solution to a System of Matrix Equations
AUTHORS:
Changzhou Dong, Yuping Zhang, Jianmin Song
KEYWORDS:
EP Matrix; Matrix Equation; Moore-Penrose Inverse; Approximation Problem; Least Squares Solution
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.3 No.4,
December
19,
2013
ABSTRACT: A square complex matrix is called if it
can be written in the form with being fixed unitary and being arbitrary matrix in . We give necessary and sufficient conditions for the
existence of the solution to the system
of complex matrix equation and present an
expression of the solution to the system
when the solvability conditions are satisfied. In addition, the solution to an
optimal approximation problem is obtained. Furthermore, the least square solution with least
norm to this system mentioned above is considered. The representation of such
solution is also derived.