# Spnull

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spnull | |

Returns a sparse orthonormal basis for the null space | |

Other toolboxes required | none |
---|---|

Related functions | sporth |

Function category | Helper functions |

License | license_spnull.txt |

This is a helper function that only exists to aid other functions in QETLAB. If you are an end-user of QETLAB, you likely will never have a reason to use this function. |

` spnull` is a function that computes an orthonormal basis for the null space of a full or sparse matrix. When the matrix is sparse, this computation is performed via the QR decomposition and is typically much faster than using

`null(full(S))`.

## Syntax

`Z = spnull(S)``Z = spnull(S,varargin)`

## Argument descriptions

`S`: The matrix to have its null space computed.`varargin`(optional): Extra arguments that, if`S`is full, will be passed to MATLAB's`null`function.

## Examples

The following example gives a 4-by-4 matrix whose null space is spanned by the two vectors $[0,0,1,0]^T$ and $[0,0,0,1]^T$:

```
>> S = sparse(4,4);
>> S(1,1) = 1; S(3,2) = 1;
>> spnull(S)
ans =
(3,1) 1
(4,2) 1
```

Note that the output is sparse because `S` is sparse. If the input is full then the output will be full as well:

```
>> spnull(full(S))
ans =
0 0
0 0
1 0
0 1
```

## Source code

Click on "expand" to the right to view the MATLAB source code for this function.

## External links

- Sparse null space and orthogonal: The source of this file on MATLAB File Exchange