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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An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
Journal of Applied Mathematics, 2014 This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices.
Tongsong Jiang, Xuehan Cheng, Sitao Ling
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Real Representation of the Polarimetric Scattering Matrix for Monostatic Radar [PDF]
Remote Sensing, 2023 Synthetic aperture radar with polarimetric diversity is a powerful tool in remote sensing. Each pixel is described by the scattering matrix corresponding to the emission/reception polarization states (usually horizontal and vertical).
Madalina Ciuca +4 more
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On the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices
Special Matrices, 2020 The singular values σ > 1 of an n × n involutory matrix A appear in pairs (σ, 1σ{1 \over \sigma }). Their left and right singular vectors are closely connected. The case of singular values σ = 1 is discussed in detail. These singular values may appear in
Faßbender Heike, Halwaß Martin
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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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Consimilarity of Commutative Quaternion Matrices [PDF]
Miskolc Mathematical Notes, 2015 Akyigit, Mahmut +2 more
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Similarity and consimilarity of hyper-dual generalized quaternions [PDF]
Mathematical Methods in the Applied SciencesThe aim of this paper is to investigate similarity and consimilarity of hyper-dual generalized quaternions and their matrices. For this purpose, we give different conjugates according to the generalized quaternionic units i,j,k.
Alagoz, Yasemin, Ozyurt, Gozde
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A Study on Commutative Elliptic Octonion Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this study, firstly notions of similarity and consimilarity are given for commutative elliptic octonion matrices. Then the Kalman-Yakubovich s-conjugate equation is solved for the first conjugate of commutative elliptic octonions. Also, the notions of
Sürekçi Arzu Cihan +1 more
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Pseudo-consimilarity and semi-consimilarity of complex matrices
Linear Algebra and its Applications, 1987 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bevis, Jean H. +2 more
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Roth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ [PDF]
, 2016 The matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0 0 B are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988)
Futorny, Vyacheslav +2 more
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