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