I'm quite out of my element trying to do some matrix calculus.
I would like to know what the derivative of $z^{T}y$ w.r.t $z$ is, where z, y are n length vectors.
Can anyone suggest good resources as well?
Thank you!
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1The derivative with respect to $z$ implies calculating the derivative in each component of $z$. for example, the derivative in component $z_1$ is $y_1$. Can you finish it from here? – Alex R. Feb 05 '17 at 00:11
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So since $z^{T}y$ is a n by n matrix do I calculate the derivative of each element w.r.t each element in $z$? – Daniel Cole Feb 05 '17 at 01:23
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$z^Ty$ is a scalar. $z$ is a vector (well, also a $n\times 1$ matrix). – Alex R. Feb 05 '17 at 01:24
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I recently posted a thorough discussion of such derivatives at http://stats.stackexchange.com/a/257616/919. Because the the map $z\to z^\prime y$ is linear, *it is its own derivative*: it linearly approximates itself. Our site has several threads on resources about matrix calculations: see http://stats.stackexchange.com/search?q=matrix+cookbook. – whuber Feb 05 '17 at 17:18