矩阵方程(AX,YA)=(B_1,B_2)的反埃尔米特广义汉密尔顿最小二乘解  

The Least Square Solution of Anti-Hermitian Generalized Hamiltonian Matrix to the Matrix Equation( AX,YA) =( B_1,B_2)

作　　者：杜玉霞[1] 尤传华[2] 梁武[1] 

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000 [2]兰州大学数学与统计学院,甘肃兰州730000

出　　处：《洛阳师范学院学报》2015年第8期5-7,共3页Journal of Luoyang Normal University

基　　金：安徽省级大学生创新创业训练项目(AH201410379078)

摘　　要：设J∈Rn×n是给定的正交反对称矩阵,即JJT=JTJ=In,JT=-J.如果矩阵A∈Cn×n满足AH=-A,JAJ=AH,称A为反埃尔米特广义汉密尔顿矩阵,所有n阶反埃尔米特广义汉密尔顿矩阵的集合记为AHHCn×n.令S=A∈AHHCn×nf(A)=‖AX-B1‖2+‖YA-B2‖2={}min.本文主要利用奇异值分解、Frobenius范数的性质和矩阵自身的结构等研究了S的解,并给出了解的表达式.Let J ∈ Rn × nbe a orthogonal anti-symmetric matrix,i. e.,JJ^T= J^TJ = In,J^T=- J. For A ∈ Cn × n. If A^H=- A,JAJ = A^H,we say that A is an anti-Hermitian generalized Hamiltonian matrix. The set of all the antiHermitian generalized Hamiltonian matrices is denoted as AHHC^n × n. Let S ={A ∈ AHHC^n × n｜f（ A） = AX- B1^2＋ YA- B2^2= }min. In this paper,we uses the singular value decomposition,the nature of Frobenius norm and the structure of anti-Hermitian generalized Hamiltonian matrix to study the solution of S,and give the expression of its solution.

关 键 词：矩阵方程 反埃尔米特广义汉密尔顿矩阵 最小 二乘解 

分 类 号：O151.21[理学—数学]