Okay so let me spell out what I have understood from your comment above, just to be clear.
If you wish you can think of the dual of a vector (a one-form) as a > one row matrix (and the vector as a one column matrix). > So, if I have column vector v = [ a1, a2, ... , an ] ' (using ' for transpose), then the dual of v is then a row vector. > If you have a scalar product operation defined there is a canonical > way to get a dual of a vector. > > For the vector v and scalar product <,>, the oneform for the vector is > v' such that v'(v) = <v, v> > So, let's say H is a nxn positive definite Hermitian matrix, and let us define the inner product < > of vectors a and b as of dimension n: <a, b> = Y* H X (where Y and X coordinate matrices of vectors a and b in some ordered basis) Then, from your comment I understand that the *dual of a vector v* is v' = <v, v> = V* H V (where V is the coordinate matrix). So it's just an inner product then? But, before you mentioned that the dual of a vector is row matrix, but as far as I understand, the inner product will just be a scalar, not a row vector. So, where is it that I am not getting you correctly? Also, I am assuming that there is a standard Hermitian matrix that is used here, like maybe the identity matrix perhaps? Also, I tried searching a bit more on Google and I found a lot of mention of the dual space, L(V, F) [ V is a vector space over the field F] which is why I am forced to believe that there might be some relation between these two (dual of a vector and dual space). Can you elaborate on this? Again I'd like to say that I am really busy with academics for next 3 weeks. So, if my replies seem to reflect thoughtlessness on my part, please excuse me for that. I just am really badly occupied. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
