Results 11 to 20 of about 161 (65)
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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Finite Iterative Algorithm for Solving a Complex of Conjugate and Transpose Matrix Equation [PDF]
Journal of Discrete Mathematics, Volume 2013, Issue 1, 2013., 2013 We consider an iterative algorithm for solving a complex matrix equation with conjugate and transpose of two unknowns of the form: A1VB1+C1WD1+A2V¯B2+C2W¯D2+A3VHB3+C3WHD3+A4VTB4 + C4WTD4 = E. With the iterative algorithm, the existence of a solution of this matrix equation can be determined automatically.
Mohamed A. Ramadan +3 more
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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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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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The Division Ring Over Conjugate Product
IEEE Access, 2019 In this paper, we investigate the rational fractions in the framework of conjugate product and establish a division ring. Some conjugate properties on the proposed division ring are obtained, and the similarity and consimilarity properties are ...
Ai-Guo Wu, Hui-Zhen Wang, Yu Teng
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Generalization of Roth's solvability criteria to systems of matrix equations [PDF]
, 2017 W.E. Roth (1952) proved that the matrix equation $AX-XB=C$ has a solution if and only if the matrices $\left[\begin{matrix}A&C\\0&B\end{matrix}\right]$ and $\left[\begin{matrix}A&0\\0&B\end{matrix}\right]$ are similar. A. Dmytryshyn and B. K{\aa}gstr\"om
Dmytryshyn, Andrii +3 more
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A Real Representation Method for Solving Yakubovich‐j‐Conjugate Quaternion Matrix Equation
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 A new approach is presented for obtaining the solutions to Yakubovich‐j‐conjugate quaternion matrix equation X−AX∧B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrix A.
Caiqin Song +4 more
wiley +1 more source
Positive Definite Solutions of the Nonlinear Matrix Equation $X+A^{\mathrm{H}}\bar{X}^{-1}A=I$ [PDF]
, 2012 This paper is concerned with the positive definite solutions to the matrix equation $X+A^{\mathrm{H}}\bar{X}^{-1}A=I$ where $X$ is the unknown and $A$ is a given complex matrix.
Cai, Guang-Bin, Lam, James, Zhou, Bin
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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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A New Solution to the Matrix Equation X−AX¯B=C
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 We investigate the matrix equation X−AX¯B=C. For convenience, the matrix equation X−AX¯B=C is named as Kalman‐Yakubovich‐conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matrices of the matrix equation.
Caiqin Song, Kaleem R. Kazmi
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