Thursday 10 April 2014

linear algebra - How to quickly find the basis of Null space in GF2

I have a matrix $A$ contains only 1 and 0. The operations is defined as in GF2, e.g., 1+0=1, 1+1=0, 0+0=0.




I know how to make $A$ into row echelon form. For example, my $A$ now becomes



1 0 0 0 0 0 1 1 1
0 1 0 0 0 1 1 1 0
0 0 1 0 0 1 1 0 1
0 0 0 1 0 1 1 0 1
0 0 0 0 1 1 0 1 1
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0


Is there a way that we can directly read the basis of Null space from this row echelon form?

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