At least in the United States, and I assume some other places as well,
matrices are usually considered to act from the left. So the kernel
of a matrix A would be the set of vectors x such that Ax = 0. In
sage, the kernel is given for the matrix acting from the right, i.e.
the set of vectors y such that yA = 0. If there is compelling
argument as to why that makes sense, I can live with it. But the
documentation for kernel() obscures, rather than clarifies, this
issue:
Docstring:
Return the kernel of x.
EXAMPLES:
sage: M = MatrixSpace(QQ,3,3)
sage: A = M([1,2,3,4,5,6,7,8,9])
sage: kernel(A)
Vector space of degree 3 and dimension 1 over Rational Field
Basis matrix:
[ 1 -2 1]
The problem with this example is that A is quite an unusual matrix:
its left-kernel is equal to its right-kernel. I recommend that a non-
square example be given that makes the current behavior clearer.
Cheers,
Marshall Hampton
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