A system of real quaternion matrix equations with applications

Wang, Qingwen; Woude, Jacob van der; Chang, Haixia

doi:10.1016/j.laa.2009.02.010

Cited by 112 publications

(47 citation statements)

References 31 publications

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“…Re-positive solution to system (1.1) of adjointable operator equations. In order to establish some necessary and sufficient conditions for system (1.1) of adjointable operator equations to have a Re-positive solution over the Hilbert C * -modules, we need the following lemma which is due to Wang et al [17].…”

Section: Elamentioning

confidence: 99%

Positive and re-positive solutions to some systems of adjointable operator equations over Hilbert C*-modules

Song¹,

Wang²

2011

ELA

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Abstract. A necessary and sufficient condition for the existence of the general common positive solution to equationsfor operators between Hilbert C * -modules is established, and an expression for the common positive solution to the equations is derived when the solvability conditions are satisfied. As an application, a new necessary and sufficient condition for the system of adjointable operator equationsover Hilbert C * -modules to have a common Re-positive solution is proved. Moreover, an expression of the general Re-positive solution is derived when the consistent conditions are met. The results of this paper extend some known results in the literature.

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Section: Elamentioning

confidence: 99%

Positive and re-positive solutions to some systems of adjointable operator equations over Hilbert C*-modules

Song¹,

Wang²

2011

ELA

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“…Applications to the operator equation AXB + CY D = E. In [13, Theorem 3.1], the general common solution of matrix equations over regular rings A 1 XB 1 = C 1 , A 2 XB 2 = C 2 is used to derive the general solution for the Sylvester equation AXB + CY D = E for matrices over regular rings. The solution derived by Wang in [13] is missing some important terms and was revised by Wang et al in [12]. We will give a complete solution below for bounded linear operators over Banach spaces.…”

Section: With V W As In (37) and Z Arbitrary Expanding The Last Eqmentioning

confidence: 99%

“…Wang presented the solvability conditions and the general solution for matrices over regular rings in [13] and this solution was revised by Wang et al in [12]. More recently, Wang and He have studied a more general matrix equation in [11].…”

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confidence: 99%

Common solutions of linear equations in a ring, with applications

Dajić

2015

ELA

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Abstract. This paper gives necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair a 1 xb 1 = c1, a 2 xb 2 = c 2 , via a simpler equation p 1 xp 2 + q 1 yq 2 =c, when each element belongs to an associative ring with unit. The paper also considers the same problem in the setting of a strongly * -reducing ring. Solutions of the generalized Sylvester equation are also presented. Both the solvability conditions and the expression for the general solution are given in terms of inner inverses. The paper uses the results obtained in the ring setting to give equivalent results for operators between Banach spaces, thus also recovering some of the well known matrix results.

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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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A system of real quaternion matrix equations with applications

Cited by 112 publications

References 31 publications

Positive and re-positive solutions to some systems of adjointable operator equations over Hilbert C*-modules

Positive and re-positive solutions to some systems of adjointable operator equations over Hilbert C*-modules

Common solutions of linear equations in a ring, with applications

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

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