On anti-centro-symmetric solutions of quaternion matrix equation AXA*=B

Ling, Sitao; Jiang, Tongsong; Shandong, Linyi

doi:10.12988/imf.2007.07147

Cited by 1 publication

(1 citation statement)

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“…• When problem 1 has a solution, write the complex representation matrix of the circulant matrix P , write the vector y according to formula (14), and then write the best approximate solution X  to P in Ω according to formula (27).…”

Section: Solving Stepsmentioning

confidence: 99%

Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

Liu,

Zhang,

Yao

et al. 2023

JAMP

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In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation − = AXB X F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation's solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method.

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Section: Solving Stepsmentioning

confidence: 99%