k次R-对称矩阵的Procrustes问题及最佳逼近问题

摘要

The class of Hermitian degree k R-symmetric matrices is characterized. Necessary and sufficient conditions and explicit formulations of Hermitian degree k R-symmetric solutions of ‖AX - V‖= min and AX = V are respectively derived, where X, V ∈ Cn×m are known matrices. For given matrix B ∈ Cn×m , the unique common Hermitian degree k R-symmetric solution of ‖AX - V‖ and ‖A - B‖ is obtained.%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∈Cn×m是已知的矩阵.给定矩阵B∈Cn×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.