scholarly journals The Least Squares Hermitian (Anti)reflexive Solution with the Least Norm to Matrix Equation AXB=C

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xin Liu ◽  
Qing-Wen Wang
Keyword(s):  
Least Squares ◽  
Explicit Expression ◽  
Matrix Equation ◽  
Kronecker Product ◽  
Complex Field ◽  
Reflection Matrix ◽  
Reflexive Matrix ◽  
Conjugate Transpose

For a given generalized reflection matrix J, that is, JH=J, J2=I, where JH is the conjugate transpose matrix of J, a matrix A∈Cn×n is called a Hermitian (anti)reflexive matrix with respect to J if AH=A and A=±JAJ. By using the Kronecker product, we derive the explicit expression of least squares Hermitian (anti)reflexive solution with the least norm to matrix equation AXB=C over complex field.

scholarly journals Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix EquationAXB+CXD=Ewith the Least Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shi-Fang Yuan
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Kronecker Product ◽  
Generalized Inverse ◽  
Complex Representation ◽  
Real Solution ◽  
Quaternion Matrix ◽  
Quaternion Matrices ◽  
Quaternion Matrix Equation ◽  
Product Of Matrices

Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution with the least norm of the quaternion matrix equationAXB+CXD=E, respectively.

scholarly journals The least squares η-Hermitian problems of quaternion matrix equation AHXA + BHYB=C

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1153-1165 ◽  
Author(s):  
Shi-Fang Yuan ◽  
Qing-Wen Wang ◽  
Zhi-Ping Xiong
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Kronecker Product ◽  
Generalized Inverse ◽  
Hermitian Matrix ◽  
Quaternion Matrix ◽  
Hermitian Matrices ◽  
Quaternion Matrices ◽  
Quaternion Matrix Equation ◽  
Product Of Matrices

For any A=A1+A2j?Qnxn and ?? {i,j,k} denote A?H = -?AH?. If A?H = A,A is called an ?-Hermitian matrix. If A?H =-A,A is called an ?-anti-Hermitian matrix. Denote ?-Hermitian matrices and ?-anti-Hermitian matrices by ?HQnxn and ?AQnxn, respectively. In this paper, we consider the least squares ?-Hermitian problems of quaternion matrix equation AHXA+ BHYB = C by using the complex representation of quaternion matrices, the Moore-Penrose generalized inverse and the Kronecker product of matrices. We derive the expressions of the least squares solution with the least norm of quaternion matrix equation AHXA + BHYB = C over [X,Y] ? ?HQnxn x ?HQkxk, [X,Y] ? ?AQnxn x ?AQkxk, and [X,Y] ? ?HQnxn x ?AQkxk, respectively.

Least Squares Skew Bisymmetric Solution for a Kind of Quaternion Matrix Equation

2011 ◽  
Vol 50-51 ◽  
pp. 190-194 ◽  
Author(s):  
Shi Fang Yuan ◽  
Han Dong Cao
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Kronecker Product ◽  
Special Structure ◽  
Complex Representation ◽  
Quaternion Matrix ◽  
Quaternion Matrices ◽  
Quaternion Matrix Equation ◽  
Product Of Matrices

In this paper, by using the Kronecker product of matrices and the complex representation of quaternion matrices, we discuss the special structure of quaternion skew bisymmetric matrices, and derive the expression of the least squares skew bisymmetric solution of the quaternion matrix equation AXB =C with the least norm.

scholarly journals Classification and approximation of solutions to Sylvester matrix equation

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4261-4280 ◽  
Author(s):  
Bogdan Djordjevic ◽  
Nebojsa Dincic
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Infinitely Many Solutions ◽  
Sylvester Matrix Equation ◽  
Minimal Norm ◽  
Sylvester Matrix

In this paperwesolve Sylvester matrix equation with infinitely-many solutions and conduct their classification. If the conditions for their existence are not met, we provide a way for their approximation by least-squares minimal-norm method.

Sign in / Sign up

Export Citation Format

Share Document