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LinKer    --    find the kernel of a matrix


Syntax 
LinKer(M: MAT): MAT

Description
This function returns a matrix whose columns represent a basis for the kernel of M. Calling the function twice on the same input will not necessarily produce the same output, though in each case, a basis for the kernel is produced.

This function works only on matrices whose entries are in a field (from version CoCoA-5.0.3). See LinKerZZ for computing a ZZ-basis for the kernel of M.

The output as it was given by CoCoA-4 (the basis of the ker) is now given by LinKerBasis . See also HilbertBasisKer .

To clarify: if K := LinKer(M); then M*K is a zero matrix.

Example 
/**/   M := mat([[1,2,3,4],[5,6,7,8],[9,10,11,12]]);
/**/   LinKer(M);
matrix(QQ,
 [[-1, -2],
  [2, 3],
  [-1, 0],
  [0, -1]])

/**/  IsZero(M*It);
true

See Also