Solution to a system of real quaternion matrix equations encompassing η-Hermicity

2015 ◽  
Vol 265 ◽  
pp. 945-957 ◽  
Author(s):  
Abdur Rehman ◽  
Qing-Wen Wang ◽  
Zhuo-Heng He
Keyword(s):  
Matrix Equations ◽  
Quaternion Matrix ◽  
Real Quaternion

scholarly journals Some quaternion matrix equations involving Φ-Hermicity

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5097-5112 ◽  
Author(s):  
Zhuo-Heng He
Keyword(s):  
Quaternion Algebra ◽  
Sufficient Conditions ◽  
Matrix Decomposition ◽  
Matrix Equations ◽  
Quaternion Matrix ◽  
Existence Of A Solution ◽  
Quaternion Matrices ◽  
Real Quaternion ◽  
Necessary And Sufficient ◽  
The Given

Let H be the real quaternion algebra and Hmxn denote the set of all m x n matrices over H. For A ? Hm x n, we denote by A? the n x m matrix obtained by applying ? entrywise to the transposed matrix At, where ? is a nonstandard involution of H. A ? Hnxn is said to be ?-Hermitian if A = A?. In this paper, we construct a simultaneous decomposition of four real quaternion matrices with the same row number (A,B,C,D), where A is ?-Hermitian, and B,C,D are general matrices. Using this simultaneous matrix decomposition, we derive necessary and sufficient conditions for the existence of a solution to some real quaternion matrix equations involving ?-Hermicity in terms of ranks of the given real quaternion matrices. We also present the general solutions to these real quaternion matrix equations when they are solvable. Finally some numerical examples are presented to illustrate the results of this paper.

scholarly journals A system of real quaternion matrix equations with applications

2009 ◽  
Vol 431 (12) ◽  
pp. 2291-2303 ◽  
Author(s):  
Qing-Wen Wang ◽  
J.W. van der Woude ◽  
Hai-Xia Chang
Keyword(s):  
Matrix Equations ◽  
Quaternion Matrix ◽  
Real Quaternion

A system of quaternary coupled Sylvester-type real quaternion matrix equations

Automatica ◽  
2018 ◽  
Vol 87 ◽  
pp. 25-31 ◽  
Author(s):  
Zhuo-Heng He ◽  
Qing-Wen Wang ◽  
Yang Zhang
Keyword(s):  
Matrix Equations ◽  
Quaternion Matrix ◽  
Real Quaternion

scholarly journals Some Theorems On Matrices With Real Quaternion Elements

1955 ◽  
Vol 7 ◽  
pp. 191-201 ◽  
Author(s):  
N. A. Wiegmann
Keyword(s):  
Similarity Transformation ◽  
Elementary Divisor ◽  
Quaternion Matrix ◽  
Unitary Similarity ◽  
Triangular Form ◽  
Quaternion Matrices ◽  
Divisor Theory ◽  
Real Quaternion ◽  
Unitary Similarity Transformation

Matrices with real quaternion elements have been dealt with in earlier papers by Wolf (10) and Lee (4). In the former, an elementary divisor theory was developed for such matrices by using an isomorphism between n×n real quaternion matrices and 2n×2n matrices with complex elements. In the latter, further results were obtained (including, mainly, the transforming of a quaternion matrix into a triangular form under a unitary similarity transformation) by using a different isomorphism.

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