Ranks and the least-norm of the general solution to a system of quaternion matrix equations

Wang, Qingwen; Li, Chengkun

doi:10.1016/j.laa.2008.05.031

Cited by 133 publications

(33 citation statements)

References 15 publications

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“…Then T, V 1 , V 2 and V 3 are invertible and by (19), (34), (37) and (38), we can get (5), (6) and (7). Also (19) follows from (11), (14), (20), (25), (35) and (36).…”

Section: Proofmentioning

confidence: 99%

An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

Wang

Woude

2011

Sci. China Math.

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We in this paper give a decomposition concerning the general matrix triplet over an arbitrary division ring F with the same row or column numbers. We also design a practical algorithm for the decomposition of the matrix triplet. As applications, we present necessary and sufficient conditions for the existence of the general solutions to the system of matrix equationsWe give the expressions of the general solutions to the system and the matrix equation when the solvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of this paper. We also mention the other applications of the equivalence canonical form, for instance, for the compression of color images. Keywords division ring, linear matrix equation, equivalence canonical form of a matrix triplet, decomposition MSC(2000): 15A21, 15A22, 15A24, 15A33, 15A03 Citation: Wang Q W, van der Woude J W, Yu S W. An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications. Sci China Math, 2011, 54(5): 907-924,

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“…Then T, V 1 , V 2 and V 3 are invertible and by (19), (34), (37) and (38), we can get (5), (6) and (7). Also (19) follows from (11), (14), (20), (25), (35) and (36).…”

Section: Proofmentioning

confidence: 99%

An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

Wang

Woude

2011

Sci. China Math.

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“…In [32], the problem of solution to the matrix equation (1.3) was considered by the Moore-Penrose generalized inverse matrix, and a general solution to this equation was obtained. In [34][35][36][37][38][39], the solutions of several quaternion matrix equations are studied. Wang [33] considered the matrix equations (1.4) over an arbitrary regular ring with identity and derived the necessary and sufficient conditions for the existence and the expression of the general solution to the system.…”

Section: Introductionmentioning

confidence: 99%

On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

Dehghan

Hajarian

2012

Linear Algebra and its Applications

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“…In the conclusion of the paper, a further research topic of investigating the extreme ranks of the solution to System (1.1) over H was proposed. Note that researches on extreme ranks, i.e., maximal and minimal ranks, of solutions to linear matrix equations have been actively ongoing for more than 30 years (see, e.g., [2][3][4][5][6][7][8][9][10][13][14][15][16][17][18][19]). In this paper, we mainly consider the extremal ranks of the general solution to (1.1).…”

Section: Introductionmentioning

confidence: 99%

Ranks of the common solution to six quaternion matrix equations

Wang

Yan

Zhang

2011

Acta Math. Appl. Sin. Engl. Ser.

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A new expression is established for the common solution to six classical linear quaternion matrixwas investigated recently by Wang, Chang and Ning (Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195: 721-732 (2008)). Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper.

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Ranks and the least-norm of the general solution to a system of quaternion matrix equations

Cited by 133 publications

References 15 publications

An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

Ranks of the common solution to six quaternion matrix equations

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