Least Squares Hermitian Problem of Matrix Equation (<i>AXB</i>, <i>CXD</i>) = (<i>E</i>, <i>F</i>) Associated with Indeterminate Admittance Matrices  

作　　者：Yanfang Liang Shifang Yuan Yong Tian Mingzhao Li 

机构地区：[1]School of Mathematics and Computational Science, Wuyi University, Jiangmen, China [2]KaiQiao Middle School in KaiPing City, Jiangmen, China

出　　处：《Journal of Applied Mathematics and Physics》2018年第6期1199-1214,共16页应用数学与应用物理（英文）

摘　　要：For A&#8712;Cm&#935;n, if the sum of the elements in each row and the sum of the elements in each column are both equal to 0, then A is called an indeterminate admittance matrix. If A is an indeterminate admittance matrix and a Hermitian matrix, then A is called a Hermitian indeterminate admittance matrix. In this paper, we provide two methods to study the least squares Hermitian indeterminate admittance problem of complex matrix equation (AXB,CXD)=(E,F), and give the explicit expressions of least squares Hermitian indeterminate admittance solution with the least norm in each method. We mainly adopt the Moore-Penrose generalized inverse and Kronecker product in Method I and a matrix-vector product in Method II, respectively.For A&#8712;Cm&#935;n, if the sum of the elements in each row and the sum of the elements in each column are both equal to 0, then A is called an indeterminate admittance matrix. If A is an indeterminate admittance matrix and a Hermitian matrix, then A is called a Hermitian indeterminate admittance matrix. In this paper, we provide two methods to study the least squares Hermitian indeterminate admittance problem of complex matrix equation (AXB,CXD)=(E,F), and give the explicit expressions of least squares Hermitian indeterminate admittance solution with the least norm in each method. We mainly adopt the Moore-Penrose generalized inverse and Kronecker product in Method I and a matrix-vector product in Method II, respectively.

关 键 词：Matrix Equation Least Squares Solution Least Norm Solution HERMITIAN INDETERMINATE ADMITTANCE MATRICES 

分 类 号：O1[理学—数学]