This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.


Basis for the null space of a matrix

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.




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.


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 :




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.

Was this topic helpful?