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C++ API

: hilb (n)

Return the Hilbert matrix of order n.

The i,j element of a Hilbert matrix is defined as

H(i, j) = 1 / (i + j - 1)

Hilbert matrices are close to being singular which make them difficult to invert with numerical routines. Comparing the condition number of a random matrix 5x5 matrix with that of a Hilbert matrix of order 5 reveals just how difficult the problem is.

cond (rand (5))
   ⇒ 14.392
cond (hilb (5))
   ⇒ 4.7661e+05

See also: invhilb.

Package: octave