Journal of Applied Mathematics

Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation A X B + C X D = E with the Least Norm

Shi-Fang Yuan

Full-text: Open access

Abstract

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 equation A X B + C X D = E , respectively.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 857081, 9 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305687

Digital Object Identifier
doi:10.1155/2014/857081

Mathematical Reviews number (MathSciNet)
MR3198408

Citation

Yuan, Shi-Fang. Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation $AXB+CXD=E$ with the Least Norm. J. Appl. Math. 2014 (2014), Article ID 857081, 9 pages. doi:10.1155/2014/857081. https://projecteuclid.org/euclid.jam/1425305687


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