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

Shi Fang Yuan; Han Dong Cao

doi:10.4028/www.scientific.net/AMM.50-51.190

Paper Titles

The Design of E-Yuan Home Multimedia System
p.171

Strongly Ding Projective, Injective and Flat Modules
p.176

Incomplete Concept Lattice Data Analytical Method Research Based on Rough Set Theory
p.180

Positive Solutions for the nth-Order Delay Differential System with Multi-Parameter
p.185

Least Squares Skew Bisymmetric Solution for a Kind of Quaternion Matrix Equation
p.190

Study on the Adaptability of Staining Method for Acoustic Field Measuring in Ultrasonic Processing
p.195

Simulations of Natural Vibration Characteristics of Large-Size Radial Gate with Three Arms Considering Fluid-Solid Coupling
p.200

The Influence of the Voltage Slope to the Homogeneous Multiple-Pulse Barrier Discharge at Atmospheric Pressure
p.205

A Study on the Acceptance and Use of Handheld E-Book Readers
p.209

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 50-51Least Squares Skew Bisymmetric Solution for a Kind...

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

Abstract:

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.

You might also be interested in these eBooks

Intelligent Structure and Vibration Control

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 50-51)

Pages:

190-194

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.50-51.190

Citation:

Cite this paper

Online since:

February 2011

Authors:

Shi Fang Yuan, Han Dong Cao

Keywords:

Least Squares Solution, Matrix Equation, Quaternion Matrices

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] Q.W. Wang: Bisymmetric and centrosymmetric solutions to system of real quaternion matrix equation, Computers Math. Applic. 49 (2005), pp.641-650.

DOI: 10.1016/j.camwa.2005.01.014

Google Scholar

[2] Y.H. Au-Yeung, C.M. Cheng: On the pure imaginary quaternionic solutions of the Hurwitz matrix equations, Linear Algebra and its Applications 419 (2006), pp.630-642.

DOI: 10.1016/j.laa.2006.06.005

Google Scholar

[3] Q. W. Wang, S .W. Yu, C.Y. Lin: Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications, Applied Mathematics and Computation, 195 (2008), pp.733-744.

DOI: 10.1016/j.amc.2007.05.018

Google Scholar

[4] T. S. Jiang, M. S. Wei: Equality constrained least squares problem over quaternion field, Applied Mathematics Letters, 16 (2003) , pp.883-888.

DOI: 10.1016/s0893-9659(03)90012-7

Google Scholar

[5] T.S. Jiang, M.S. Wei: Real representations of quaternion matrices and quaternion matrix equations, Acta Math Sci (China) 26 A (2006), pp.578-584.

Google Scholar

[6] Yao tang Li and Wen jing Wu. Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations. Computers Mathematics with Applications, 55 (2008), pp.1142-1147.

DOI: 10.1016/j.camwa.2007.06.015

Google Scholar

[7] S.F. Yuan, A.P. liao, Y. Lei: Least squares Hermitian solution of the matrix equation with the least norm over the skew field of quaternions, Mathematical and Computer Modelling 48(2008), pp.91-100.

DOI: 10.1016/j.mcm.2007.08.009

Google Scholar

[8] S. F. Yuan, A.P. Liao, Y. Lei: Minimization problem for Hermitian matrices over the quaternion field, Mathematica Acta Scientia, 29A (2009), pp.1298-1306. (in Chinese).

Google Scholar

[9] H. Dai and P. Lancaster: Linear matrix equations from an inverse problem of vibration theory, Linear Algebra and Its Applications, 246 (1996), pp.31-47.

DOI: 10.1016/0024-3795(94)00311-4

Google Scholar

[10] J.R. Magnus: L-structured matrices and linear matrix equations, Linear and Multilinear Algebra 14 (1983).

DOI: 10.1080/03081088308817543

Google Scholar