Rob Beezer wrote: > I've put together a quick reference sheet (two pages) for linear > algebra commands in Sage. I'll do a bit more clean-up on this before > posting a final copy on the wiki in a couple days, so I know there is > a bit more work to do. Specifically, I might reorder the sections if > I come up with a more logical presentation. > > I'd really like to hear about any glaring omissions, or gross > misunderstandings of categories, vector spaces, modules, rings and/or > fields. Draft copy at > > http://buzzard.ups.edu/sage/quickref-linalg.pdf > > Thanks, > Rob >
Nice! Comments: * The first entry of a vector is not 0! (zero factorial :), but zero. Unfortunately, it seems like it is always confusing to read mathematics that has exclamation points. Same comment for the matrix section. * u.norm() == u.norm() ? That seems confusing. Do you mean something like u.norm(2)? * A.inverse should have parentheses (i.e., A.inverse() ) * under row operations, "e.g." should be followed with a comma * You might mention the very powerful and intuitive indexing and setting available using the bracket notation. See the docstrings of __getitem__ and __setitem__ in sage/matrix/matrix0.pyx for lots and lots of examples. This notation puts us roughly on par with octave and matlab for easy creation of submatrices and setting elements of a submatrix. * in eigenmatrix_right/left, P may not have eigenvectors. If the algebraic multiplicity does not equal the geometric multiplicity for a particular eigenspace, then P pads the eigenvectors with zero vectors so that you still have AP=PD (for _right). If A is diagonalizable, then your statement is correct; the columns of P are eigenvectors of A. * Some of the decompositions don't work for all base rings; you might mention that (e.g., QQ doesn't have SVD) * .change_right(R) has unnecessary commas around the last "R" in the explanation Again, very nice! I will probably use this in the next few weeks. Thanks, Jason --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en -~----------~----~----~----~------~----~------~--~---
