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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Modern Package Design Using Digital 3D Image Processing Technique
Mobile Information Systems, Volume 2022, Issue 1, 2022., 2022 In the extensive age, dear designate perplexity and relatively supercilious show charge in the traditive parcel extend project composition, the double discriminator GAN is ply to the bale work indicate composition. On the basis of BicycleGAN, a topic discriminator is added, and the analogous privation sine and external province are reformed.
Shengying Feng +5 more
wiley +1 more source
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
core +3 more sources
Polarimetric Analysis Using the Algebraic Real Representation of the Scattering Matrix
2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, 2021 Equivalent matrix representations in radar polarimetry have long been studied and used as tools for modeling and understanding the scattering mechanisms.
Madalina Ciuca +4 more
semanticscholar +1 more source
Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras [PDF]
, 2017 For each two-dimensional vector space $V$ of commuting $n\times n$ matrices over a field $\mathbb F$ with at least 3 elements, we denote by $\widetilde V$ the vector space of all $(n+1)\times(n+1)$ matrices of the form $\left[\begin{smallmatrix}A&*\\0&0 ...
Futorny, Vyacheslav +3 more
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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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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
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 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
wiley +1 more source
On the Gersgorin Theorem applied to Radar Polarimetry [PDF]
, 2007 This contribution is concerned with the mathematical formulation and theoretical background of the ...
Boerner, Wolfgang-Martin +2 more
core +1 more source