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A note on quaternion matrices and split quaternion matrix pencils
Journal of Applied Mathematics and Computing, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical Journal of Okayama University, 1997
If \(H^{m\times n}\) denotes the set of all \(m\times n\) matrices over the quaternion field \( H\), a matrix \(A,A\in H^{m\times n},\) is \text{Re}-nonnegative definite if \(\text{Re}\to(X^{\ast }AX)\geqslant 0\) holds for every \(X\in H^{m\times 1}\), where \(X^{\ast }\)\ denotes the conjugate transpose of \(X\). The author finds the set of all \text{
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If \(H^{m\times n}\) denotes the set of all \(m\times n\) matrices over the quaternion field \( H\), a matrix \(A,A\in H^{m\times n},\) is \text{Re}-nonnegative definite if \(\text{Re}\to(X^{\ast }AX)\geqslant 0\) holds for every \(X\in H^{m\times 1}\), where \(X^{\ast }\)\ denotes the conjugate transpose of \(X\). The author finds the set of all \text{
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L-structured quaternion matrices and quaternion linear matrix equations
Linear and Multilinear Algebra, 2015This paper focuses on L-structured quaternion matrices. L-structured real matrices, conditions for the existence of solutions and the general solution of linear matrix equations were studied in the paper [Magnus JR. L-structured matrices and linear matrix equations, Linear Multilinear Algebra 1983;14:67–88].
Shi-Fang Yuan, Qing-Wen Wang
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A Matrix Defined by the Quaternion Group
The American Mathematical Monthly, 1902(1902). A Matrix Defined by the Quaternion Group. The American Mathematical Monthly: Vol. 9, No. 11, pp. 243-248.
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Solvability of a quaternion matrix equation
Applied Mathematics-A Journal of Chinese Universities, 2002The author studies the solvability of the matrix equations \((*)\) \(AXB=D\) and \((**)\) \(A^*X^*B^*\pm BXA=D\) where \(A\), \(B\), \(D\) are quaternion matrices. He gives necessary and sufficient conditions for the solvability of \((*)\) (resp. of \((**)\)) in Hermitian and in skew-Hermitian matrices (resp.
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Finite quaternionic matrix groups
Representation Theory, 1998Let D \mathcal {D} be a definite quaternion algebra such that its ...
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Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory
Journal of Mathematical Physics, 2005By means of complex representation and real representation of a quaternion matrix, this paper studies the problem of diagonalization of a quaternion matrix, gives two algebraic methods for diagonalization of quaternion matrices in quaternionic quantum theory.
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Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm
IEEE Transactions on Image Processing, 2022Jifei Miao, Kit Ian Kou
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Matrix Representation of Dual Quaternions
2013After a review of some properties of dual quaternions, De Moivre's and Euler's formulas for the matrices associated with these quaternions are studied. In special case, De Moivre's formula implies that there are uncountably many matrices of unit dual quaternions satisfying 4 n A I = for n≥3.
JAFARI, Mehdi +2 more
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Quaternion-Based Bilinear Factor Matrix Norm Minimization for Color Image Inpainting
IEEE Transactions on Signal Processing, 2020Jifei Miao, Kit Ian Kou
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