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
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
doaj +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
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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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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
A Note on the Solutions of Some Linear Octonionic Equations [PDF]
, 2014 The main concerns of this paper are the linear equations with one term and one unknown of the forms: a(xa) =r, a(xb ) = r and (ax)b =r, and the linear equations with two terms and one unknown of the forms: (ax)b +(g x)d =r and a (xb )+g (xd ) =r over the
Bolat, Cennet, İpek, Ahmet
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Regularizing algorithm for mixed matrix pencils [PDF]
, 2017 P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker's canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability.
Klymchuk, Tetiana
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