A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation
A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrix A. The closed form solution is establi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/285086 |
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| Summary: | A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion
matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared
to the existing results, there are no requirements on the coefficient matrix A. The closed
form solution is established and the equivalent form of solution is given for this Yakubovich-j-conjugate
quaternion matrix equation. Moreover, the existence of solution to complex conjugate
matrix equation X−AX¯B=CY is also characterized and the solution is derived in an explicit
form by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrix
equation over complex field is a special case of Yakubovich-j-conjugate quaternion matrix equation
X−AX^B=CY. Numerical example shows the effectiveness of the proposed results. |
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| ISSN: | 1085-3375 1687-0409 |