On Dec 18, 2008, at 12:12 AM, Jason Grout wrote > Oh, I understood the above to mean that you could define a matrix B, > for > example, without defining the elements of the matrix. I don't know > how > to do that in Mathematica; maybe I'm confused.
It's actually done implicitly, see: http://reference.wolfram.com/mathematica/tutorial/MultiplyingVectorsAndMatrices.html So, D[Transpose[a].B.c, c] should just work. > At any rate, for now, > I'll assume that you mean that you define "vectors" a and c and a > "matrix" B in Mma by specifying the entries as symbolic > expressions. I > put vectors and matrix in quotes since I just ran into some trouble > trying to do an example session in Mma. To my knowledge, Mma really > has > no notion of a "vector" or a "matrix", but instead has just the notion > of a list and a list of lists. This gave me problems in trying to do > what what you did below. Here, I define n to be a "vector" and try to > compute NN^T > > In[2]:= n = {1, t, Cos[t]} > > Out[2]= {1, t, Cos[t]} > > In[3]:= b=n.Transpose[n] > > Transpose::nmtx: > The first two levels of the one-dimensional list {1, t, Cos[t]} > cannot be transposed. > Yeah, that won't work since they aren't defined as a vector. > > Instead, I assume you mean to define n as literally a column vector > (i.e., a column "matrix")? > Yes, I mean a column vector/matrix. > In[6]:= n = {{1, t, Cos[t]}}//Transpose > > Out[6]= {{1}, {t}, {Cos[t]}} > > In[7]:= b=n.Transpose[n] > > 2 2 > Out[7]= {{1, t, Cos[t]}, {t, t , t Cos[t]}, {Cos[t], t Cos[t], > Cos[t] }} > > >> D[Transpose[a].B.c, c] >> or >> D[Transpose[a].B.c, a] >> >> If they conform, the operation is valid, and has a simple solution. > > Pardon my ignorance, but what do you mean by a "solution"? Do you > mean > that the derivatives yield a result, or that there is another solving > step which involves an equation? > I mean that the derivatives yield a result. > I think that this might be possible in Sage using > http://trac.sagemath.org/sage_trac/ticket/3941 and > http://trac.sagemath.org/sage_trac/ticket/4493. Can you give a > specific > Mathematica example session? I'll try to duplicate it in Sage. > The problem is that I don't have a copy of Mathematica any more. I last had a license for version 4 for a different machine that I don't use anymore. I know the first ticket isn't what I mean, I'm not sure about the second. I want to define a set of column vectors, a, c, and N (without specifying the length aside from it being length n or contents). Then, perform a^T.N.N^T.c (1xn).(nx1).(1xn).(nx1) = 1x1 so everything conforms. and carry out the derivative with respect to the vectors c or a. This derivative is easy to carry out by hand, but since the operations aren't really supported, it isn't easily done in most CAS packages. I hope this helps clarify things. Cheers, Tim. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
