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On pointwise and analytic similarity of matrices

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Abstract

LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈ p B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a B(ε) ifB(ε)=T(ε)A(ε)T −1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈ a B(ε) provided thatA(ε)≈ p B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the origin and was first stated by Wasow.

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References

  1. F. R. Gantmacher,The Theory of Matrices, Vol. I, Chelsea, New York, 1964.

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  2. M. Marcus and H. Minc,A Survey of Matrix Theory and Matrix Inequalities, Prindle, Weber and Schmidt, 1964.

  3. W. Wasow,On holomorphically similar matrices, J. Math. Anal. Appl.4 (1962), 202–206.

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  4. W. Wasow,Topics in the theory of linear ordinary, differential equations having singularities with respect to a parameter, IRMA, Universite Louis Pasteur, Strasbourg, 1978.

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Sponsored by the United States Army under Contract No. DAAG29-75-C-0024

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Friedland, S. On pointwise and analytic similarity of matrices. Israel J. Math. 35, 89–108 (1980). https://doi.org/10.1007/BF02760940

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  • DOI: https://doi.org/10.1007/BF02760940

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