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A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application [PDF]
Mathematics, 2022 We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix
Long-Sheng Liu +2 more
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Variational solution of the
, 2005 We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and frequency.
I. A. Nechaev, Е. В. Чулков
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A New Solution to the Matrix Equation X−AX¯B=C [PDF]
The Scientific World Journal, 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
Caiqin Song
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On the Yang-Baxter-like matrix equation for rank-two matrices
Open Mathematics, 2017 Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX.
Zhou Duanmei, Chen Guoliang, Ding Jiu
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A Survey on Solving the Matrix Equation AXB = C with Applications
MathematicsThis survey provides a comprehensive overview of the solutions to the matrix equation AXB=C over real numbers, complex numbers, quaternions, dual quaternions, dual split quaternions, and dual generalized commutative quaternions, including various special
Qing-Wen Wang, Lv-Ming Xie, Zi-Han Gao
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Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space
Mathematics, 2023 The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems.
Dijana Mosić +2 more
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AIMS Mathematics, 2022 In this paper, we consider the common Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions to a pair of linear matrix equations $ A_1XA_1^\ast = C_1, \ A_2XA_2^\ast = C_2 $ and present some necessary and sufficient conditions for ...
Yinlan Chen, Lina Liu
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On spectral numerical method for variable-order partial differential equations
AIMS Mathematics, 2022 In this research article, we develop a powerful algorithm for numerical solutions to variable-order partial differential equations (PDEs). For the said method, we utilize properties of shifted Legendre polynomials to establish some operational matrices ...
Kamal Shah +3 more
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AIMS Mathematics, 2022 In this paper, we propose an efficient method for some special solutions of the quaternion matrix equation AXB+CYD=E. By integrating real representation of a quaternion matrix with H-representation, we investigate the minimal norm least squares solution ...
Anli Wei +3 more
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An Exact Solution to a Quaternion Matrix Equation with an Application
Symmetry, 2022 In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of quaternion matrix equations
Long-Sheng Liu +3 more
semanticscholar +1 more source