NULL

Purpose:

Computes an orthogonal basis for the Null space of an array.

Syntax:

NULL(a)

 

a  -  An input array.

Returns:

An orthogonal array of n columns where n is the Null space size.

Example:

a = {{1, 2, 3},

     {4, 5, 6}, 

     {7, 8, 9}} 

 

b = null(a)

 

returns {-0.408248, 0.816497, -0.408248}

b' *^ b returns {1}

a *^ b returns {1.332268E-015, 8.881784E-016, 0.0}

Remarks:

NULL uses SVD to compute the orthogonal basis. The number of output columns is the dimension of the Null space. The number of output rows is the number of input columns.

 

If b = null(a) exists, the output columns of b are orthogonal and have a norm of 1 such that:

 

conj(b') *^ b == eye(numcols(b)), the identity matrix.

See Also:

NORM

ORTH

RANK

SVD