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Hilbert matrix
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(Definition)
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A Hilbert matrix of order is a square matrix defined by
An example of a Hilbert matrix when is
Hilbert matrices are ill-conditioned.
The inverse of a Hilbert matrix
is given by
An example of an inverted Hilbert matrix when case is:
For more fun with Hilbert matrices, see [1].
- 1
- Choi, Man-Duen. Tricks or Treats with the Hilbert Matrix. American Mathematical Monthly 90, 301-312, 1983.
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"Hilbert matrix" is owned by Daume. [ full author list (2) | owner history (1) ]
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(view preamble)
Cross-references: inverse, ill-conditioned, square matrix, order
There are 3 references to this entry.
This is version 3 of Hilbert matrix, born on 2002-09-28, modified 2005-06-24.
Object id is 3479, canonical name is HilbertMatrix.
Accessed 11733 times total.
Classification:
| AMS MSC: | 65F35 (Numerical analysis :: Numerical linear algebra :: Matrix norms, conditioning, scaling) | | | 15A12 (Linear and multilinear algebra; matrix theory :: Conditioning of matrices) | | | 15A09 (Linear and multilinear algebra; matrix theory :: Matrix inversion, generalized inverses) | | | 15A57 (Linear and multilinear algebra; matrix theory :: Other types of matrices ) |
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Pending Errata and Addenda
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