Actually, that's a good point. What we need for SymPy, as I've noted before, is a minimal set of identities from which the rest can be derived. I think what is needed is a simple minimal set of identities, which are all derived manually from the definitions, and then the rest which are just shown algebraically from those identities. Seeing those derivations explicitly should make it easier to understand how to implement them. Let us know if you find a good resource.
Aaron Meurer On Sat, May 3, 2014 at 9:12 PM, Tim Lahey <[email protected]> wrote: > On 3 May 2014, at 22:52, Alan Bromborsky wrote: > >> X <#>LatexIt! run report... >> >> >> *** Found expression $ij$ >> >> The basic definition should be that the directional derivative of of a >> matrix valued function of a matrix is >> >> $$ \lim_{h\rightarrow 0} \frac{F(A+hB)}{h}$$ >> >> where the directional derivative is in the direction of the matrix $B$ and >> $A$ and $B$ must have the same dimension. The if $B$ is decomposed into >> components $B_{ij}$ (components of a vector or matrix) then >> >> >> $$\lim_{h\rightarrow 0}\frac{F(A+hB_{ij})}{h}$$ >> >> are the $ij$ components of the derivative. I did not put any expression >> to the left of the limits due to notational uncertainty. > > > This is the basics, which I understand quite well. The problem is that the > Matrix Cookbook has lots of identities which are just stated, many of which > involve inverses and transposes (sometimes at the same time), so it's not a > simple exercise to derive them. > > The one in the issue that Aaron referenced > > diff(A.T*x,x) = A.T > > which I guess the Cookbook had as A (not A.T), is simple enough. It's quite > easy to derive and show that it should be A.T for a general matrix. > > It seems that there isn't one good reference for general matrix calculus. It > seems that there's individual references for specific aspects. I've looked > through most of the Wikipedia page references, I'll have to look through the > references for the Matrix Cookbook next. > > Thanks, > > Tim. > > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/F9C1C872-E83E-4423-81F4-A15BF061DFF6%40gmail.com. > > For more options, visit https://groups.google.com/d/optout. -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6Ke-u7NfQP%3DnQLFMf-xQh5KUx9KpZXEEH-EMNejBdqq%2Bg%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
