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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Conpseudosimilarity and consemisimilarity over a division ring [PDF]
, 1990 It is shown that for n × n matrices over a division ring which is finite dimensional over its center, the notions of consimilarity, conpseudosimilarity and consemisimilarity are all equivalent, provided the conjugation is ...
Bevis, Jean H. +2 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
أسرار التشابه اللفظي في تفسير الشيخ الشعراوي المتعلقة بالتذكير والتأنيث (دراسة وصفية تحليلية): Secrets of Consimilarity in the Exegesis of Sheikh Shaarawi related to Masculinity & Femininity (An Analytical Descriptive Study) [PDF]
, 2022 The Holy Qur’an is Allah’s miraculous book for his creation in its composing, style, eloquence and organization, miraculous in its wisdom and knowledge, and as a unique way of guidance according to times and circumstances.
Abdullah, Dr. Naveed Altaf Khan
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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
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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RNA‐Based Assessment of Diversity and Composition of Active Archaeal Communities in the German Bight
Archaea, Volume 2012, Issue 1, 2012., 2012 Archaea play an important role in various biogeochemical cycles. They are known extremophiles inhabiting environments such as thermal springs or hydrothermal vents. Recent studies have revealed a significant abundance of Archaea in moderate environments, for example, temperate sea water.
Bernd Wemheuer +3 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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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
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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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