Matrix Calculus

[xdmatheusw]

I have a question about the derivative of the dot product of two vectors. if I have f(w, y) = w' * y where w and y are vectors, why is the derivative of f(w, y) relative to w is y and not y'? (y' is the transpose of y) thanks for listening.

 

[Deleted member 4993]

I have a question about the derivative of the dot product of two vectors. if I have f(w, y) = w' * y where w and y are vectors, why is the derivative of f(w, y) relative to w is y and not y'? (y' is the transpose of y) thanks for listening.


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[xdmatheusw]

Sorry, i will try to explain it better.

I was studying machine learnig and I came across a linear regression problem, and I was following the proof for the optimization problem. I will link the proof below.



My question is on line 5.10, where the derivative of 2 * w' * X' * y is equal to 2 * X' * y.

I think that the product of X' by y will result in a vector, and following the definition of the derivative of a scalar by a vector, the result would have to be transposed, in the case X' * y, where it would be y' * X