I am confused with something rather simple which is embarrassing..
Let G=A(Yμ).
G is p by 1 matrix depending on β=[β0 β1 β(p1)]'. (β is p by 1)
Α is p by n matrix depending on β
μ is n by 1 matrix depending on β
Υ is n by 1 matrix independent of β
I thought the derivative of G with respect to β (let dG) would be
dG=(dA)*(Yμ)Α*dμ.
which is obviously wrong because the dG should be a p by p matrix.
Α*dμ is p by p (which is encouraging!)
but (Yμ) is n by 1 and the dimensions would not agree.
I checked the following:
http://en.wikipedia.org/wiki/Matrix_calculus
but did't get it..
I checked my calculus book of Ross and Finley and doesn't have anything.
I checked my algebra book of Gilbert Strang and doesn't have anything.
I searched the net with no luck
and I decided to make an example in matlab, so just see how can I get the derivative of a matrix with respect to a vector I typed
>> syms b0 b1 real
>> b=[b0 b1]';
>> A=[b0*b1 b0*b1];
>> diff(A,'b')
ans =
[ 0, 0]
which is not what I want. diff just fount=d the difference of the elements right? I would like the 2 by 2 derivative matrix of A with respect to b.
My final goal is to get right the derivative of G=A(Yμ) right.
Thanx in advance for any answers.
