TITLE:
Least Squares Hermitian Problem of Matrix Equation (AXB, CXD) = (E, F) Associated with Indeterminate Admittance Matrices
AUTHORS:
Yanfang Liang, Shifang Yuan, Yong Tian, Mingzhao Li
KEYWORDS:
Matrix Equation, Least Squares Solution, Least Norm Solution, Hermitian Indeterminate Admittance Matrices
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
14,
2018
ABSTRACT: For A∈CmΧn, 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.