#5135: Alternative basis for kernel of a matrix
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Reporter: rbeezer | Owner: rbeezer
Type: enhancement | Status: new
Priority: minor | Milestone: sage-feature
Component: linear algebra | Keywords: kernel, basis
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The left_kernel() method in matrix2.pyx computes basis vectors from the
reduced echelon form of the transposed matrix. For each non-pivot column,
the corresponding entry of a basis vector is set to 1, the other non-pivot
columns are set to zero, and the remaining entries are set to negatives of
other specific entries of the matrix.
This basis is then used in a constructor of a subspace, and the basis is
"echelonized" in the process. Add a new keyword argument, echelonize, to
left_kernel, that defaults to true. With echelonize=false, the subspace
will be constructed with the "pivot" basis and it will not be further
massaged.
Sage-devel discussion [http://groups.google.com/group/sage-
devel/browse_thread/thread/3d934669e00978e1/ here].
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5135>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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