洛阳师范学院学报
洛暘師範學院學報
락양사범학원학보
Journal of Luoyang Normal University
2015年
8期
5-7
,共3页
矩阵方程%反埃尔米特广义汉密尔顿矩阵%最小%二乘解
矩陣方程%反埃爾米特廣義漢密爾頓矩陣%最小%二乘解
구진방정%반애이미특엄의한밀이돈구진%최소%이승해
matrix equation%anti-Hermitian generalized Hamiltonian matrix%least square solution
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×n f（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．
設J∈Rn×n是給定的正交反對稱矩陣，即JJT ＝JTJ ＝In，JT ＝－J．如果矩陣A∈Cn×n滿足AH ＝－A， JAJ ＝AH，稱A為反埃爾米特廣義漢密爾頓矩陣，所有n階反埃爾米特廣義漢密爾頓矩陣的集閤記為AHHCn×n．令S ＝ A∈AHHCn×n f（A）＝‖AX －B1‖2＋‖YA －B2‖2＝min ．本文主要利用奇異值分解、Frobenius範數的性質和矩陣自身的結構等研究瞭S的解，併給齣瞭解的錶達式．
설J∈Rn×n시급정적정교반대칭구진，즉JJT ＝JTJ ＝In，JT ＝－J．여과구진A∈Cn×n만족AH ＝－A， JAJ ＝AH，칭A위반애이미특엄의한밀이돈구진，소유n계반애이미특엄의한밀이돈구진적집합기위AHHCn×n．령S ＝ A∈AHHCn×n f（A）＝‖AX －B1‖2＋‖YA －B2‖2＝min ．본문주요이용기이치분해、Frobenius범수적성질화구진자신적결구등연구료S적해，병급출료해적표체식．
Let J∈Rn×n be a orthogonal anti-symmetric matrix, i.e., JJT =JTJ =In,JT =-J .For A∈Cn×n .If AH =-A,JAJ =AH , we say that A is an anti-Hermitian generalized Hamiltonian matrix .The set of all the anti-Hermitian generalized Hamiltonian matrices is denoted as AHHCn ×n . Let S=A∈AHHCn×n f(A) =AX -B12 +YA -B22 =min .In this paper, we uses the singular value decomposi-tion, 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 .
