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On Complex Split Quaternion Matrices [PDF]

Advances in Applied Clifford Algebras, 2013
Soon after Hamilton's discovery of the quaternion algebra, James Cockle introduced the so-called split quaternions: they have the same vector space but one defines \(i^2=-1\), \(j^2=k^2=1\), \(ijk=1\). Split quaternions also do not obey the commutative law, but there are divisors of zero, nilpotent elements and nontrivial idempotents. Furthermore, they
Melek Erdogdu, Mustafa Özdemir, Özdemir Mustafa   +2 more
exaly   +3 more sources

On Eigenvalues of Split Quaternion Matrices [PDF]

Advances in Applied Clifford Algebras, 2013
A method for finding left eigenvalues of split quaternion matrices is established. Existence of right eigenvalues of a split quaternion matrix satisfying some equation is proved. The authors also show that the Gershgorin theorem which provides an inclusion disc for left eigenvalues of quaternion matrices also holds for split quaternion matrices.
Melek Erdogdu, Mustafa Özdemir, Özdemir Mustafa   +2 more
exaly   +4 more sources

On the eigenvalues of quaternion matrices [PDF]

Linear and Multilinear Algebra, 2011
This article is a continuation of the article [F. Zhang, Gersgorin type theorems for quaternionic matrices, Linear Algebra Appl. 424 (2007), pp. 139–153] on the study of the eigenvalues of quaternion matrices. Profound differences in the eigenvalue problems for complex and quaternion matrices are discussed.
Farid, F. O., Wang, Qing-Wen, Zhang, Fuzhen   +2 more
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On Hyperbolic Split Quaternions and Hyperbolic Split Quaternion Matrices [PDF]

Advances in Applied Clifford Algebras, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
ALAGÖZ, Yasemin, Özyurt, Gözde
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Solving Quaternion Linear System Based on Semi-Tensor Product of Quaternion Matrices [PDF]

Symmetry, 2022
In this paper, we use semi-tensor product of quaternion matrices, L-representation of quaternion matrices, and GH-representation of special quaternion matrices such as quaternion (anti)-centrosymmetric matrices to solve the special solutions of ...
Xueling Fan, Zhao Jianli
exaly   +2 more sources

Split Quaternion Matrix Representation of Dual Split Quaternions and Their Matrices [PDF]

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erdoğdu, Melek, Özdemir, Mustafa
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Littlewood's algorithm and quaternion matrices [PDF]

Linear Algebra and Its Applications, 1999
A strengthened form of Schur's triangularization theorem is given for quaternion matrices with real spectrum (for complex matrices it was given by Littlewood).
Dennis Merino, Vladimir Sergeichuk
exaly   +2 more sources

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Consimilarity of quaternions and coneigenvalues of quaternion matrices

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sitao Ling, Xuehan Cheng, Tongsong Jiang
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Commutativity for Matrices of Quaternions

Canadian Journal of Mathematics, 1968
For any ring we shall denote by the ring of all n × n matrices with elements from and by the set of all polynomials in x with coefficients from . will denote the non-commutative four-dimensional division algebra of real quaternions with 1, i1, i2, i3 as ...
Carlson, R. E., Cullen, C. G.
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Quaternions and Matrices

2020
This chapter contains some basic knowledge on quaternions, Toeplitz and Hankel matrices and we introduce some useful maps which allow to consider, instead of quaternionic matrices, complex matrices of double size. For more information about quaternionic matrices, the interested reader may consult, e.g., Rodman’s book [97]. We also recall the notions of
Daniel Alpay, Fabrizio Colombo, Irene Sabadini   +2 more
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