nullspace ( matrix -- seq )

Vocabulary

math.matrices.elimination

Inputs

matrix

a sequence

Outputs

seq	a sequence

Word description

Computes a basis for the nullspace of a matrix. Each returned vector has one element per column and its product with the matrix is zero. A matrix with linearly independent columns has an empty nullspace basis, as does an empty matrix. The input matrix is modified during elimination.

Examples

USING: math.matrices.elimination prettyprint ; { { 1 2 } } nullspace .
{ { -2 1 } }

Definition

USING: kernel math.matrices sequences ;

IN: math.matrices.elimination

: nullspace ( matrix -- seq )
    echelon reduced dup empty? [
        dup first length <identity-matrix> [
            [ dup leading drop [ basis-vector ] [ drop ] if* ]
            each
        ] with-matrix flip nonzero-rows
    ] unless ;