The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations

Xie, Dongxiu; Hu, Xi-Yan; Sheng, Yanping

doi:10.1016/j.laa.2006.01.027

Cited by 27 publications

(14 citation statements)

References 6 publications

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“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]). In mathematics, engineering, and others, many problems can be transformed into some linear matrix equations.…”

Section: Remark 11mentioning

confidence: 99%

Theη-bihermitian solution to a system of real quaternion matrix equations

Wang

2013

Linear and Multilinear Algebra

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Let H m×n be the set of all m × n matrices over the real quaternion algebra.We in this paper, present the solvability conditions and the general η-Hermitian solution to a system of linear real quaternion matrix equations. As an application, we give the necessary and sufficient conditions for the systemWe establish an expression of the η-bihermitian to the system when it is solvable. We also obtain a criterion for a quaternion matrix to be η-bihermitian. Moreover, we provide an algorithm and a numerical example to illustrate the theory developed in this paper.

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“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]). In mathematics, engineering, and others, many problems can be transformed into some linear matrix equations.…”

Section: Remark 11mentioning

confidence: 99%

Theη-bihermitian solution to a system of real quaternion matrix equations

Wang

2013

Linear and Multilinear Algebra

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“…The problem has been studied for different structured matrices. We refer the reader to [12][13][14][15][16][17] and the references therein. However, they consider only the first modification of some models and have not studied the perturbation of the modified solution.…”

Section: Introductionmentioning

confidence: 99%

A numerical method of structure-preserving model updating problem and its perturbation theory

Xie

2011

Applied Mathematics and Computation

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“…[13][14][15][16][17][18]26,[35][36][37][38][39][40][41][42][43][44][45][46]. The frequently studied Lyapunov equation BX + (BX ) * = A constitutes a major function in mathematics, such as optimal control, stability analysis, system theory, model reduction; see, e.g, [19,20].…”

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confidence: 99%