Creates a Hilbert matrix.
an integer value, the dimension of the square matrix.
In linear algebra, a Hilbert matrix is a matrix with the unit fraction elements.
The Hilbert matrices are canonical examples of ill-conditioned matrices, making them notoriously difficult to use in numerical computation. For example, the 2-norm condition number of a 5x5 Hilbert matrix above is about 4.8e5.
The Hilbert matrix is symmetric and positive definite.
hilbert generates a Hilbert matrix of order
Hilbert D., Collected papers, vol. II, article 21.
Beckermann B, (2000); The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numerische Mathematik 85, 553–577, 2000.
Choi, M.D., (1983); Tricks or Treats with the Hilbert Matrix, American Mathematical Monthly 90, 301–312, 1983.
Todd, J., (1954); The Condition Number of the Finite Segment of the Hilbert Matrix, National Bureau of Standards, Applied Mathematics Series 39, 109–116.
Wilf, H.S., (1970); Finite Sections of Some Classical Inequalities, Heidelberg, Springer.
1 2 3
## Create a Hilbert Matrix: H = hilbert(5) H
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