Some matrix equations with applications†

Wang, Qingwen; He, Zhuo-Heng

doi:10.1080/03081087.2011.648635

Cited by 51 publications

(24 citation statements)

References 41 publications

(27 reference statements)

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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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“…Then we can give some necessary and sufficient conditions for the existence of the general solutions to the real quaternion matrix equations (1.3) and (1.4) in terms of the ranks of the given coefficient matrices. There have been many papers using different approaches to investigate the matrix equations and real quaternion matrix equations involving η-Hermicity (e.g., [9]- [14], [16]- [23], [33]- [49]). The rest of this paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous decomposition of quaternion matrices involving η-Hermicity with applications

Wang

Zhang

2017

Applied Mathematics and Computation

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“…Ding et al presented iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle [36]. Moreover, other matrix equations such as descriptor linear systems and quaternion matrix equations have also been investigated [37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Parametric Solutions to the Generalized Discrete Yakubovich‐Transpose Matrix Equation

Song¹,

Feng²,

Wang³

et al. 2013

Asian Journal of Control

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This paper is concerned with the complete parametric solutions to the generalized discrete Yakubovich‐transpose matrix equation X − AXTB = CY. which is related with several types of matrix equations in control theory. One of the parametric solutions has a neat and elegant form in terms of the Krylov matrix, a block Hankel matrix and an observability matrix. In addition, the special case of the generalized discrete Yakubovich‐transpose matrix equation, which is called the Karm‐Yakubovich‐transpose matrix equation, is considered. The explicit solutions to the Karm‐Yakubovich‐transpose matrix equation are also presented by the so‐called generalized Leverrier algorithm. At the end of the paper, two examples are given to show the efficiency of the proposed algorithm.

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Some matrix equations with applications†

Cited by 51 publications

References 41 publications

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

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

Simultaneous decomposition of quaternion matrices involving η-Hermicity with applications

Parametric Solutions to the Generalized Discrete Yakubovich‐Transpose Matrix Equation

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