Least Squares Hermitian Problem of Matrix Equation (AXB, CXD) = (E, F) Associated with Indeterminate Admittance Matrices - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.6, June 2018

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

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DOI: 10.4236/jamp.2018.66101 671 Downloads 1,465 Views

Author(s)

Yanfang Liang^1,2, Shifang Yuan^1*, Yong Tian¹, Mingzhao Li¹

Affiliation(s)

¹School of Mathematics and Computational Science, Wuyi University, Jiangmen, China.
²KaiQiao Middle School in KaiPing City, Jiangmen, China.

ABSTRACT

For A∈C^mΧn, 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.

KEYWORDS

Matrix Equation, Least Squares Solution, Least Norm Solution, Hermitian Indeterminate Admittance Matrices

Share and Cite:

Liang, Y. , Yuan, S. , Tian, Y. and Li, M. (2018) Least Squares Hermitian Problem of Matrix Equation (AXB, CXD) = (E, F) Associated with Indeterminate Admittance Matrices. Journal of Applied Mathematics and Physics, 6, 1199-1214. doi: 10.4236/jamp.2018.66101.

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