A question about computing bases for kernels or null spaces of matrices. When working with students studying linear algebra for the first time, I like to construct basis vectors for the (right) kernel by working through the indices of the non-pivot columns of the reduced row echelon form of the matrix, setting these entries to zero, with the exception of one entry that is set to 1. Then the other entries are just negatives of certain entries of the echelon form matrix.
This very approach is used (on the transpose) to compute the (left) kernel. But then it gets used in the constructor of a subspace, which calls a submodule constructor, which "echelonizes" the basis (presumably to achieve some canonical representation). This means the kernel produces a vector space with a very nice basis, but my students won't recognize it. I'd like to get the pivot/non-pivot basis back. Could the construction of the pivot/non-pivot basis be isolated from the kernel() code in matrix2.pyx? And maybe called nullspace_basis () or something similar? Then kernel() could call this method on the transpose, and use the result to construct the subspace. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
