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linalg(deprecated)

 hilbert
 create a Hilbert matrix

 Calling Sequence hilbert(n) hilbert(n, x)

Parameters

 n - positive integer x - (optional) expression

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $\mathrm{hilbert}\left(3\right)$
 $\left[\begin{array}{ccc}{1}& \frac{{1}}{{2}}& \frac{{1}}{{3}}\\ \frac{{1}}{{2}}& \frac{{1}}{{3}}& \frac{{1}}{{4}}\\ \frac{{1}}{{3}}& \frac{{1}}{{4}}& \frac{{1}}{{5}}\end{array}\right]$ (1)
 > $\mathrm{hilbert}\left(3,x+1\right)$
 $\left[\begin{array}{ccc}\frac{{1}}{{1}{-}{x}}& \frac{{1}}{{2}{-}{x}}& \frac{{1}}{{3}{-}{x}}\\ \frac{{1}}{{2}{-}{x}}& \frac{{1}}{{3}{-}{x}}& \frac{{1}}{{4}{-}{x}}\\ \frac{{1}}{{3}{-}{x}}& \frac{{1}}{{4}{-}{x}}& \frac{{1}}{{5}{-}{x}}\end{array}\right]$ (2)