# Derivative Hadamard Product

$\tfrac{\mathrm{d} }{\mathrm{d} W } (\vec{a}W) \odot (\vec{b}W)$

I am looking for the solution of this derivative of the Hadamard Product.
a and b are vectors of dimension |V|, W is a Matrix with dimension |V|×|d|
• What do you mean with the derivative wrt W?

• I did d some research and it seems to me that there is no commonly accepted definition. Please provide one.

• The term is part of the backpropagation of my neural network. I need to calculate this derivative to update my weights in the neural network. Hope this helps.

• The hadamard product is the elemt-wise product of two matrices of the same dimensionality https://en.m.wikipedia.org/wiki/Hadamard_product_(matrices)

• One can view the product as a function from R^(|V|\times |d|) to R^(|d|). So the derivative may mean just the matrix of partial derivatives. Do you expect the result to be a a |d| by ( |V|\times |d| ) matrix?

• a and b must be row vectors for this product to make sense.

• Ideally the result would be in the dimenson of |V|

• The preferred notation for a vector is as a column vector, so ideally aW would be written as a^t W , meaning a transpose times W. will keep with the notation you used, so that aW is a row vector times a matrix, but this is not a very common notation.

• I will keep with the notation you used, so that aW is a row vector times a matrix, but this is not a very common notation*

• I am sorry for any inconvenience with the notation. Of course, a and b would be transposed.

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