<hilbert-matrix> ( m n -- matrix )
Extra matrix operations

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Vocabulary
math.matrices.extras

Inputs

m	an integer
n	an integer

Outputs

matrix

a matrix

Word description
A Hilbert matrix is a square-matrix A in which entries are the unit fractions A[i][j] = 1/(i+j-1). See hilbert matrix.

A Hilbert matrix is a special case of the <hankel-matrix>.

Examples

USING: math.matrices.extras prettyprint ; 1 2 <hilbert-matrix> .
{ { 1 1/2 } }

USING: math.matrices.extras prettyprint ; 3 6 <hilbert-matrix> .
{ { 1 1/2 1/3 1/4 1/5 1/6 } { 1/2 1/3 1/4 1/5 1/6 1/7 } { 1/3 1/4 1/5 1/6 1/7 1/8 } }

Definition

USING: kernel math sequences ;

IN: math.matrices.extras

: <hilbert-matrix> ( m n -- matrix )
    [ <iota> ] bi@ [ + 1 + recip ] cartesian-map ;