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Formulae for estimating extreme changes of lengths in spatial affine transformation

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Summary

Formulae (27) and (28) which make it possible to estimate the minimum and maximum value of the deformation in length in affine transformation in space have been derived. Both values are determined by means of the elements of the given transformation matrixA without having to form the productAA T, or compute the corresponding eigenvalues explicitly. The derived formulae hold true under the assumption that both extreme values do not differ from each other too much.

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Reference

  1. J. H. Wilkinson: The Algebraic Eigenvalue Problem. Clarendon Press, Oxford 1965.

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Authors and Affiliations

  1. Research Institute of Geodesy, Prague

    František Charamza

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  1. František Charamza
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Dedicated to 90th Birthday of Professor František Fiala

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Charamza, F. Formulae for estimating extreme changes of lengths in spatial affine transformation. Stud Geophys Geod 17, 165–169 (1973). https://doi.org/10.1007/BF01613686

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  • DOI: https://doi.org/10.1007/BF01613686

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