Journal ArticleDOI
On Complex Split Quaternion Matrices
Melek Erdoğdu,Mustafa Özdemir +1 more
TLDR
In this paper, it was shown that any complex split quaternion has a 4 × 4 complex matrix representation and that BA = I is true for complex-split quaternions.Abstract:
In this paper, we present some important properties of complex split quaternions and their matrices. We also prove that any complex split quaternion has a 4 × 4 complex matrix representation. On the other hand, we give answers to the following two basic questions “If AB = I, is it true that BA = I for complex split quaternion matrices?” and “How can the inverse of a complex split quaternion matrix be found?”. Finally, we give an explicit formula for the inverse of a complex split quaternion matrix by using complex matrices.read more
Citations
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Journal ArticleDOI
On Hermitian Solutions of the Split Quaternion Matrix Equation $$AXB+CXD=E$$ A X B + C X D = E
TL;DR: In this paper, the authors discuss Hermitian solutions of split quaternion matrix equation and establish a necessary and sufficient condition for the existence of a solution and a solution formula, and provide numerical algorithms and numerical examples to illustrate the results.
Journal ArticleDOI
Algebraic methods for least squares problem in split quaternionic mechanics
TL;DR: By means of complex representation and real representation of a split quaternion matrix, two algebraic methods for finding solutions of the problems insplit quaternionic mechanics are derived.
Journal ArticleDOI
Consistency of Split Quaternion Matrix Equations $$AX^{\star }-XB=CY+D$$ A X ⋆ - X B = C Y + D and $$X-AX^\star B=CY+D$$ X - A X ⋆ B = C Y + D
Xin Liu,Yang Zhang +1 more
TL;DR: In this article, the authors derived necessary and sufficient conditions for the existence of solutions to the above two split quaternion matrix equations and their special cases, and also obtained some conditions for these four split matrix equations to be uniquely solvable.
Journal ArticleDOI
On the split quaternion matrix equation $$AX=B$$AX=B
Xin Liu,Zhuo-Heng He +1 more
TL;DR: In this paper, the authors considered the split quaternion matrix equation and derived the expressions of solutions when equation is solvable, where the solvability conditions and expression of the unique solution X or X=\pm X^{\star }$$ were given.
References
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Journal ArticleDOI
Quaternions and matrices of quaternions
TL;DR: A brief survey on quaternions and matrices of quaternion is given in this article, where the authors present new proofs for certain known results and discuss the quaternionic analogues of complex matrices.
Book
Quaternionic and Clifford Calculus for Physicists and Engineers
TL;DR: Quanternions and multivectors Clifford Valued Functions and Forms Clifford Operator Calculus Boundary Value Problems Numerical Clifford Analysis Further Results and Research Problems Appendices Index as mentioned in this paper