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.
Highlights
Recall that an n n complex matrix A is called EP if AA† A† A
Has attracted many people’s attention and many results have been obtained about system (2) with various constraints, such as bisymmetric, Hermitian, positive semidefinite, reflexive, and generalized reflexive solutions, and so on
It is well-known that EP matrices are a wide class of objects that include many matrices as their special cases, such as Hermitian and skew
Summary
Recall that an n n complex matrix A is called EP (or range Hermitian) if AA† A† A. Has attracted many people’s attention and many results have been obtained about system (2) with various constraints, such as bisymmetric, Hermitian, positive semidefinite, reflexive, and generalized reflexive solutions, and so on (see, [9,10,11,12]). It is well-known that EP matrices are a wide class of objects that include many matrices as their special cases, such as Hermitian and skew-. Least squares solution, which can be described as follows: Let nep n U denote the set of all EPr matrices with fixed unitary matrix U in n n , SL. Throughout we denotes n n ep the set of all EPr matrices with fixed unitary matrix U in n n , i.e.,
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