矩阵方程（AX，YA）＝（B1，B2）的反埃尔米特广义汉
密尔顿最小二乘解
杜玉霞;尤传华;梁武
【期刊名称】《洛阳师范学院学报》 【年(卷),期】2015(000)008
【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×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．%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 . 【总页数】3页(5-7)
【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 【作者】杜玉霞;尤传华;梁武
矩阵方程(AX,YA)=(B1,B2)的反埃尔米特广义汉密尔顿最小二乘解
