Abstract:

Hermitian antireflexive (antiHermitian antireflexive) least squares solutions of matrix equations (AX=B, XC=D) were considered. With special properties of partitioned matrices and Hermitian antireflexive (antiHermitian antireflexive) matrices, the general expression of the solution was obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set was considered.

Key words: matrix equations, Hermitian antireflexive matrix, antiHermitian antireflexive matrix, least squares solution, optimal approximation