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SAGE + right_kernel() + basis matrix

I executed the right_kernel() instruction for any binary matrix H. Why always I get a basis matrix in this form [I|A] (Where I:identity matrix)?

Solution

  • In general it is not the case that the basis matrix has the form [I|A].

    According to the sage documentation the basis matrix is in echelon form by default.

    For example

    sage: H
[1 0 0 1 1]
[1 0 1 0 1]
[1 0 0 0 0]
sage: H.right_kernel()
Vector space of degree 5 and dimension 2 over Finite Field of size 2
Basis matrix:
[0 1 0 0 0]
[0 0 1 1 1]