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In linear algebra, a Hilbert matrix, introduced by Hilbert, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, being notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8×105.

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rdfs:label	Hilbert matrix (en)
rdfs:comment	In linear algebra, a Hilbert matrix, introduced by Hilbert, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, being notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8×105. (en)
sameAs	Hilbert matrix Hilbert matrix
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Cite_book dbt:Cite_journal dbt:E dbt:Harvs dbt:Harvtxt dbt:OEIS2C dbt:Matrix_classes
Subject	Approximation theory Determinants Matrices Numerical linear algebra
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Hilbert_matrix?oldid=1047876481&ns=0
Wikipage page ID	265000 (xsd:integer)
page length (characters) of wiki page	6779 (xsd:nonNegativeInteger)
Wikipage revision ID	1047876481 (xsd:integer)
Link from a Wikipage to another Wikipage	Unit fraction Acta Mathematica Approximation theory Binomial coefficient Approximation theory Determinants Cauchy matrix Glaisher–Kinkelin constant Matrices Numerical linear algebra Main diagonal Method of moments (statistics) Definite matrix Linear algebra Square matrix Closed-form expression Condition number On-Line Encyclopedia of Integer Sequences Gram matrix Symmetric matrix Determinant Factorial Hankel matrix Invertible matrix Stirling's approximation Totally positive matrix Least squares Matrix (mathematics) Polynomial
has abstract	In linear algebra, a Hilbert matrix, introduced by Hilbert, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, being notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8×105. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Hilbert_matrix
is Wikipage redirect of	Hilbert matrices
is Link from a Wikipage to another Wikipage of	List of things named after David Hilbert Cauchy matrix Jacobi eigenvalue algorithm David Hilbert Lehmer matrix Method of mean weighted residuals List of functional analysis topics List of mathematical examples List of named matrices List of numerical analysis topics Condition number Hilbert matrices H-matrix Hankel matrix
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Hilbert_matrix

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