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Macaulay2Doc :: kernel(Matrix)

kernel(Matrix) -- kernel of a matrix

Synopsis

Description

If f is a ring element, then it will be interpreted as a one by one matrix.

The kernel is the submodule of M of all elements mapping to zero under f. Over polynomial rings, this is computed using a Gröbner basis computation.

i1 : R = ZZ/32003[vars(0..10)]

o1 = R

o1 : PolynomialRing
i2 : M = genericSkewMatrix(R,a,5)

o2 = | 0  a  b  c  d |
     | -a 0  e  f  g |
     | -b -e 0  h  i |
     | -c -f -h 0  j |
     | -d -g -i -j 0 |

             5       5
o2 : Matrix R  <--- R
i3 : ker M

o3 = image {1} | gh-fi+ej  |
           {1} | -dh+ci-bj |
           {1} | df-cg+aj  |
           {1} | -de+bg-ai |
           {1} | ce-bf+ah  |

                             5
o3 : R-module, submodule of R

See also