Solution to Several Split Quaternion Matrix Equations
MathematicsSplit 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 properties.
Xin Liu, Tong Shi, Yang Zhang
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An Efficient Method for Split Quaternion Matrix Equation X − Af(X)B = C
Symmetry, 2022 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 using the real representation of split quaternion matrices, H representation method, the Kronecker ...
Shufang Yue +3 more
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Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations
Journal of MathematicsIn this article, we use the real representation matrix of the split quaternion matrix, vector operator, Kronecker product, and Moore–Penrose generalized inverse.
Yang Zhang, Xiaoda Zhang
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Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics
Journal of Mathematics, 2023 The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical
Tongsong Jiang +4 more
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Order 3 elements in G2 and idempotents in symmetric composition algebras [PDF]
, 2017 Order three elements in the exceptional groups of type G2 are classified up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is obtained. Idempotents
Elduque, Alberto
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Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring [PDF]
, 2015 We show that two blocks of generalized quaternion defect with three simple modules over a sufficiently large 2-adic ring O are Morita-equivalent if and only if the corresponding blocks over the residue field of O are Morita-equivalent.
Eisele, F.
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Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]
Notes on Number Theory and Discrete MathematicsThis paper introduces the Generalized Tribonacci Hybrid Split Quaternion (GTHSQ), a novel split quaternion with coefficients derived from generalized Tribonacci hybrid numbers.
Yanni Yang, Yong Deng
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Low-lying zeros of L-functions for Quaternion Algebras [PDF]
, 2018 The density conjecture of Katz and Sarnak predicts that, for natural families of L-functions, the distribution of zeros lying near the real axis is governed by a group of symmetry.
Lesesvre, Didier
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Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4 [PDF]
, 2007 Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a p-adic ring.
Broué +6 more
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On the Consimilarity of Split Quaternions and Split Quaternion Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion ...
Kösal Hidayet Hüda +2 more
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