On the determinant of quaternionic polynomial matrices and its application to system stability [PDF]
, 2008 In this paper, we propose a definition of determinant for quaternionic, polynomial matrices inspired by the well-known Dieudonne determinant for the constant case.
Paula Rocha +3 more
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Some New Properties of The Real Quaternion Matrices and Matlab Applications
Cumhuriyet Science Journal, 2019 In this study, firstly, it was shown that the set of real quaternionmatrices is a -dimensional module over the real matrix ring and -dimensional module over the complex matrix ring .
Kemal Gökhan Nalbant, Salim Yüce
doaj +1 more source
Quaternion equations and quaternion polynomial matrices [PDF]
, 2013 We mainly consider finding formula solutions to quaternion equations and calculating the generalized inverses of quaternion polynomial matrices.
Huang, Liji
openaire +2 more sources
Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion ...
Kosal Hidayet Huda, Tosun Murat
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Right linear map preserving the left spectrum of 2x2 quaternion matrices; pp. 378–386 [PDF]
Proceedings of the Estonian Academy of Sciences, 2018 In this paper, the form of a right linear map preserving the left spectrum of quaternion matrices of order 2 is characterized. The obtained conclusion is different from the classical results of the linear map preserving eigenvalues of complex matrices.
Deyu Duan +3 more
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Stability of quaternionic linear systems [PDF]
, 2006 The main goal of this paper is to characterize stability and bounded-input-bounded-output (BIBO)-stability of quaternionic dynamical systems. After defining the quaternion skew-field, algebraic properties of quaternionic polynomials such as divisibility ...
Vettori, Paolo, Pereira, Ricardo
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Determinants and multiplicative functionals on quaternion matrices [PDF]
, 2003 Determinants of matrices over a field are multiplicative. Does there exist an extension of the definition of determinants of real matrices to quaternion matrices, such that the multiplication theorem holds?
Fan, Jiangnan
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Polar decompositions of quaternion matrices in indefinite inner product spaces [PDF]
, 2021 Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an H-polar decomposition are found.
Ran, André C.M. +6 more
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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
Special Matrices, 2014 L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331(2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix ...
Klimchuk Tatiana, Sergeichuk Vladimir V.
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(R2050) Dual Quaternion Matrices and MATLAB Applications [PDF]
, 2023 There are many studies in the literature on real quaternions and real quaternion matrices. There are few studies in the literature on dual quaternions. Definitions of the matrices of dual quaternions used in this study will be given.
Nalbant, Kemal Gökhan, Yüce, Salim
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