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The condition numbers of the matrix eigenvalue problem

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Summary

For ann ×n matrixA with distinct eigenvalues explicit expressions are obtained for certain condition numbers associated with the reduction ofA to its Jordan normal form. These condition numbers are also related by inequalities to (i) the departure from normality ofA, (ii) the discriminant of the eigenvalues ofA, (iii) the Gram determinant of the eigenvectors ofA.

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  1. Deparment of Mathematics University of Durham, Durham, Great Britain

    R. A. Smith

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  1. R. A. Smith
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Smith, R.A. The condition numbers of the matrix eigenvalue problem. Numer. Math. 10, 232–240 (1967). https://doi.org/10.1007/BF02162166

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  • DOI: https://doi.org/10.1007/BF02162166

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