Results 1 to 10 of about 83 (82)
, 2020 Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure.
Christine Tobler +2 more
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Special MatricesThis paper provides a complete characterization of the real matrices A for which the equation p(X) = A has a real solution X∈Mn(R) $X\in {M}_{n}\left(\mathbb{R}\right)$ for every nonconstant polynomial p∈R[x] $p\in \mathbb{R}\left[x\right]$ .
Zhu Chengyi
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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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Cramer's rule for a class of coupled Sylvester commutative quaternion matrix equations
Demonstratio MathematicaIn this article, based on the real representation and Kronecker product, Cramer’s rule for a class of coupled Sylvester commutative quaternion matrix equations is studied and its expression is obtained.
Cai Xiaomin, Ke Yifen, Ma Changfeng
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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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Demonstratio MathematicaGiven a square matrix AA, we are able to construct numerous equalities involving reasonable mixed operations of AA and its conjugate transpose A∗{A}^{\ast }, Moore-Penrose inverse A†{A}^{\dagger } and group inverse A#{A}^{\#}. Such kind of equalities can
Tian Yongge
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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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IEEE Access, 2018 This paper is concerned with the numerical solutions of the general matrix equation $\sum ^{p}_{i=1}{\sum ^{s_{i}}_{j=1} }\,\,{A_{ij}X_{i}}{B_{ij}} = C$ , and the general discrete-time periodic matrix equations $\sum ^{p}_{i=1}\sum ^{s_{i}}_{j=1} (A_{i,
Basem I. Selim, Lei Du, Bo Yu
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A projector oriented approach to the best linear unbiased estimator
General Gauss–Markov model, Ordinary least squares estimator, Oblique projector, Generalized projection operator, 62J05, 62H12, 15A24, 15A57,
Oskar Baksalary, Götz Trenkler
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Distributive and Dual Distributive Elements in Hyperlattices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and ∨-semi hyperlattice, respectively.
Ameri Reza +3 more
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