Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A result on the singularities of matrix functions

Author: William T. Reid
Journal: Quart. Appl. Math. 35 (1977), 293-296
MSC: Primary 34B05
DOI: https://doi.org/10.1090/qam/442340
MathSciNet review: 442340
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Abstract: For $ F\left( t \right) = F\left( {{t_1},...,{t_p}} \right)$ an $ n \times n$ complex-valued matrix function which is continuous on an open neighborhood of $ {t^0} = \left( {{t_\alpha }^0} \right)\left( {\alpha = 1,...,p} \right)$ and singular at $ {t^0}$ there is presented a necessary and sufficient condition for $ F\left( t \right)$ to be non-singular on a deleted neighborhood of $ {t^0}$. If, in addition, $ F(t)$ is differentiate at $ {t^0}$ then a corollary to this criterion yields a differential condition that is sufficient for such isolation of a point of singularity. Applications of corollary are given, including in particular for $ n = 1$ the correction of a result stated by George and Gunderson [1].

References [Enhancements On Off] (What's this?)

  • [1] J. H. George and R. W. Gunderson, An existence theorem for linear boundary value problems, Quart. Appl. Math. 31, 127-131 (1973) MR 0463554
  • [2] H. F. Mathis, A theorem on the extension of a rectangular matrix of continuous functions to become a nonsingular square matrix, Proc. Amer. Math. Soc. 1, 344-345 (1950) MR 0036823
  • [3] W. T. Reid, Ordinary differential equations, John Wiley and Sons, New York, 1971 MR 0273082
  • [4] F. V. Atkinson, Discrete and continuous boundary problems, Academic Press, New York, 1964 MR 0176141

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DOI: https://doi.org/10.1090/qam/442340
Article copyright: © Copyright 1977 American Mathematical Society

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