It should be lightly easier than it is to convert a vector of length n to either an nx1 matrix or a 1xn matrix:
sage: v = vector(srange(5)) sage: v (0, 1, 2, 3, 4) sage: matrix(QQ,1,5,[v]) [0 1 2 3 4] sage: matrix(QQ,5,1,list(v)) [0] [1] [2] [3] [4] I got neither of those right the first time! I know that v*v is short for the dot product, which is also (row v)*(col v), but sometimes one wants (col v)*(row v) as a rank 1 nxn matrix: sage: matrix(QQ,5,1,list(v)) * matrix(QQ,1,5,[v]) [ 0 0 0 0 0] [ 0 1 2 3 4] [ 0 2 4 6 8] [ 0 3 6 9 12] [ 0 4 8 12 16] I suggest that vector methods row_matrix() and col_matrix() would be useful. John 2008/9/7 Jason Merrill <[EMAIL PROTECTED]>: > > On Sep 6, 7:26 pm, Jason Merrill <[EMAIL PROTECTED]> wrote: >> Is there a simple way to think of the difference between a vector with >> n elements, and a 1 by n matrix in Sage. When would I want to use one >> instead of the other? >> >> sage: m = matrix([1,2,3,4,5]) >> sage: parent(m) >> Full MatrixSpace of 1 by 5 dense matrices over Integer Ring >> >> sage: v = vector([1,2,3,4,5]) >> sage: parent(v) >> Ambient free module of rank 5 over the principal ideal domain Integer >> Ring >> >> m seems to have many more methods than v, but looking at matrix? and >> vector? didn't make things perfectly clear. > > mhansen caught up with me on IRC and cleared things up a bit. I > thought I'd paste in the conversation for the benefit of any others > who are wondering. > > [9:22pm] mhansen: jwmerrill: I don't know if I understand your > question about matrices and vectors. What are you trying to do? > [9:22pm] mhansen: "Vectors" in Sage are elements of a free module / > vector space. > [9:23pm] mhansen: One usually thinks about matrices as representing > homomorphisms between such spaces. > [10:01pm] jwmerrill: mhansen: re vectors/matrices, I'm not trying to > do anything too specific > [10:01pm] jwmerrill: just trying to fit my head around sage > [10:02pm] mhansen: Well, they're very different mathematical objects > that just happened to have 5 "numbers" associated with them. > [10:04pm] jwmerrill: fair enough > [10:05pm] mhansen: Addition is defined component-wise for both of them > and they both support scalar multiplication. > [10:05pm] jwmerrill: can you right multiply either of them by an > appropriately sized matrix? > [10:06pm] mhansen: Yep. > [10:06pm] mhansen: Vectors have no notion of being a "row vector" or > "column vector". > [10:06pm] jwmerrill: oh, that's interesting > [10:07pm] mhansen: So, if you have a vector of size n, you can act on > it on either side with an nxn matrix. > [10:08pm] jwmerrill: ok > [10:08pm] mhansen: Multiplying two vectors is a shortcut for the inner > product on that space (typically the standard dot product). > [10:09pm] jwmerrill: got it > [10:09pm] jwmerrill: one of the things I was wondering about was what > kind of sage object should represent the type of thing that ode > solvers would want as the jacobian > [10:11pm] jwmerrill: in practice, it has to be a function that returns > a collection of numbers > [10:11pm] jwmerrill: when evaluated at some point > [10:11pm] jwmerrill: is that more like a vector, or a matrix? > [10:12pm] jwmerrill: Hubbard and Hubbard makes a point of making the > distinction that the gradient is a vector, but the jacobian is a row > matrix > [10:13pm] jwmerrill: but I didn't really get what the point was, other > than that the gradient can change if you have a different inner > product rule, but the jacobian doesn't need any inner product at all > [10:15pm] mhansen: Yes, I would do the Jacobian as a matrix. > [10:15pm] mhansen: You can evaluate matrices over the symbolic ring in > Sage. > [10:15pm] mhansen: sage: m = matrix(SR, [[x, x+1],[2*x,0]]); m > [10:15pm] mhansen: [ x x + 1] > [10:15pm] mhansen: [ 2*x 0] > [10:15pm] mhansen: sage: m(2) > [10:15pm] mhansen: [2 3] > [10:16pm] mhansen: [4 0] > [10:16pm] jwmerrill: ok, cool > > JM > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
