# Documentation

### This is machine translation

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

# `linalg`::`nullspace`

Basis for the null space of a matrix

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

## 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)`

## 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`.