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phubaba
Posts:
4
Registered:
2/11/08


matrix differentials
Posted:
May 10, 2010 1:01 PM


Hello everyone,
I've been trying to learn matrix calculus in my free time, and I've been struggling with one general concept.
Given that you have a matrix differential example:
P = Nx1, V=NxN, V is a matrix of constants P is variable
then dP'VP =d(P'V)P+P'd(VP) =d(P')*VP + P'dV*P+P'dV*P + P'VdP (second and third terms are 0 because dV is zero) = d(P')*V*P + P'VdP
now my question is how do we manipulate the term d(P')*V*P . I know that the solution to the above derivative is: P'(V'+V). Therefore d(P')*V*P must equal P'V'd(P).
However, it is not clear to me how this is done. http://ht.econ.kobeu.ac.jp/~tanizaki/workshop/2007/20070309.pdf does something similar on page 23 example 5.2. This is also done in http://research.microsoft.com/enus/um/people/minka/papers/matrix/minkamatrix.pdf on page 3.



