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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)).


  • 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.


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 here to view this function's source code on github.

External links