k次R-对称矩阵的Procrustes问题及最佳逼近问题

Procrustes Problem of Hermitian Degree k R-symmetric Matrix and Its Approximation Problem

刻画了Hermitian k次R-对称矩阵,并分别给出AX=V和‖AX-V‖=min存在Hermitian k次R-对称解的充要条件和解的精确表达式,其中X,V∈C^(n×m)是已知的矩阵.给定矩阵B∈C^(n×n),该文给出‖AX-V‖=min和‖A-B‖=min存在公共的Hermitian k次R-对称解的充要条件和解的表达式.

The class of Hermitian degree k R-symmetric matrices is characterized.Necessaryand sufficient conditions and explicit formulations of Hermitian degree k R-symmetric solutionsof‖AX-V‖=min and AX=V are respectively derived,where X,V∈C^n×mare knownmatrices.For given matrix B∈C^n×n,the unique common Hermitian degree k R-symmetricsolution of‖AX-V‖and‖A-B‖is obtained