How well-conditioned can the eigenvector problem be?

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URI: https://hdl.handle.net/10902/28468
ISSN: 0025-5718
ISSN: 1088-6842
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Autoría
Beltrán Álvarez, CarlosAutoridad Unican; Bétermin, Laurent; Grabner, Peter; Steinerberger, Stefan
Fecha
2022
Derechos
© American Mathematical Society. First published in Mathematics of computation in volume 91, number 335, published by the American Mathematical Society
Publicado en
Mathematics of Computation, 2022, 91(335), 1237-1245
Editorial
American Mathematical Society
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Resumen/Abstract
The condition number for eigenvector computations is a well– studied quantity. But how small can it possibly be?: Specifically, what matrices are perfectly conditioned with respect to eigenvector computations? In this note we answer this question for n × n matrices, giving a solution that is exact to first-order as n → ∞.
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