Least squares X=±Xη* solutions to split quaternion matrix equation AXAη*=B
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DOI: 10.1002/mma.6033
Abstract: In the paper, the split quaternion matrix equation AXAη*=B is considered, where the operator Aη* is the η‐conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which well exploited the special structures… read more here.
Keywords: least squares; matrix equation; equation; quaternion matrix ... See more keywords
A New Polar Representation for Split and Dual Split Quaternions
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DOI: 10.1007/s00006-017-0797-8
Abstract: We present a new different polar representation of split and dual split quaternions inspired by the Cayley–Dickson representation. In this new polar form representation, a split quaternion is represented by a pair of complex numbers,… read more here.
Keywords: split quaternion; split; dual split; polar representation ... See more keywords
On Hermitian Solutions of the Split Quaternion Matrix Equation $$AXB+CXD=E$$AXB+CXD=E
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DOI: 10.1007/s00006-017-0806-y
Abstract: In this paper, we discuss Hermitian solutions of split quaternion matrix equation $$AXB+CXD=E,$$AXB+CXD=E, where X is an unknown split quaternion Hermitian matrix, and A, B, C, D, E are known split quaternion matrices with suitable size. The objective of… read more here.
Keywords: split quaternion; axb; hermitian solutions; axb cxd ... See more keywords
Elementary Transformation and its Applications for Split Quaternion Matrices
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DOI: 10.1007/s00006-019-1027-3
Abstract: In this paper, the elementary transformation is discussed for split quaternion matrices and the upper triangulation process is given. Then two new determinants are defined by means of real and complex representation matrices and the… read more here.
Keywords: quaternion; split quaternion; elementary transformation; transformation applications ... See more keywords
Solution to Several Split Quaternion Matrix Equations
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DOI: 10.3390/math12111707
Abstract: Split quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental… read more here.
Keywords: quaternion matrix; matrix equations; split quaternion;
An Efficient Method for Split Quaternion Matrix Equation X - Af(X)B = C
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DOI: 10.3390/sym14061158
Abstract: In this paper, we consider the split quaternion matrix equation X−Af(X)B=C, f(X)∈{X,XH,XiH,XjHXkH}. The H representation method has the characteristics of transforming a matrix with a special structure into a column vector with independent elements. By… read more here.
Keywords: quaternion matrix; split quaternion; matrix equation; equation ... See more keywords
The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra
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DOI: 10.3390/sym16040491
Abstract: In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB = C, and present the general solution expression when the solvability conditions are met. As an application, we… read more here.
Keywords: equation; dual split; algebra; split quaternion ... See more keywords