Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[HilbertMatrix], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The function hilbert returns the n x n generalized Hilbert matrix.

This matrix is symmetric and has $\frac{1}{i+j-x}$ as its (i, j)th entry.  If x is not specified, $x=1$ is used.

The command with(linalg,hilbert) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$\mathrm{hilbert}\left(3\right)$

$\left[\begin{array}{ccc}1& \frac{1}{2}& \frac{1}{3}\\ \frac{1}{2}& \frac{1}{3}& \frac{1}{4}\\ \frac{1}{3}& \frac{1}{4}& \frac{1}{5}\end{array}\right]$

$\mathrm{hilbert}\left(3\,x+1\right)$

$\left[\begin{array}{ccc}\frac{1}{1-x}& \frac{1}{2-x}& \frac{1}{3-x}\\ \frac{1}{2-x}& \frac{1}{3-x}& \frac{1}{4-x}\\ \frac{1}{3-x}& \frac{1}{4-x}& \frac{1}{5-x}\end{array}\right]$