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linalg::nullspace

Basis for the null space of a matrix

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Syntax

linalg::nullspace(A)

Description

linalg::nullspace(A) returns a basis for the null space of the matrix A, i.e., a list B of linearly independent vectors such that if and only if is a linear combination of the vectors in B.

The component ring of the matrix A must be a field, i.e., a domain of category Cat::Field.

If the component ring of A does not have a canonical representation of the zero element, it can happen that linalg::nullspace does not find a basis for the null space. In such a case, a wrong result is returned.

Examples

Example 1

The kernel of the matrix:

A := Dom::Matrix(Dom::Real)( 
  [[3^(1/2)*2 - 2, 2], [4, 3^(1/2)*2 + 2]] 
)

is one-dimensional, and a basis is :

linalg::nullspace(A)

Related Examples

Parameters

A

A matrix of a domain of category Cat::Matrix

Return Values

List of (column) vectors of the domain Dom::Matrix(R), where R is the component ring of A.

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