# Spnull

 Other toolboxes required spnull Returns a sparse orthonormal basis for the null space none sporth Helper functions 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.