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THE DRAZIN INVERSE OF MATRICES OF QUATERNIONS

THE DRAZIN INVERSE OF MATRICES OF QUATERNIONS
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摘要 Let H be the real quaternion field,C and R be the complex and real field respectively.Clearly R(?)C(?)H. Let H<sup>m×n</sup> denote the set of all m×n matrices over H.If A=(a<sub>rs</sub>)∈H<sup>m×n</sup>,then there exist A<sub>1</sub> and A<sub>2</sub>∈C<sup>m×n</sup> such that A=A<sub>1</sub>+A<sub>2</sub>j.Let A<sub>C</sub> denote the complexrepresentation of A,that is the 2m×2n complex matrix Ac=((A<sub>1</sub>/A<sub>2</sub>)(-A<sub>2</sub>/A<sub>1</sub>))(see[1,2]).We denote by A<sup>D</sup> the Drazin inverse of A∈H<sup>m×n</sup> which is the unique solution of the e-
基金 Supported by the Natural Science Foundation of jiangxi
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参考文献1

  • 1Liao Zuhua.Group inverses and Drazin inverses of morphisms with equivalence factorizations[].Journal of Nanchang Univerwity(Natural Science)setp.1995

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