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Suppose we have a function of two n-dimensional vectors [tex]f(\mathbf{x},\mathbf{y})[/tex]. How can we find the gradient and Hessian of this function?

Regards

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Suppose we have a function of two n-dimensional vectors [tex]f(\mathbf{x},\mathbf{y})[/tex]. How can we find the gradient and Hessian of this function?

Regards

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mathwonk

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So, the gradient will be 1-by-2n vector, and the Hessian will be 2n-by-2n matrix?

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mathwonk

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I.e. if R^n = V, the 1st derivative is a linear map VxV-->R, and the second derivative is a symmetric bilinear map (VxV)x(VxV)-->R.

So if you really want to break up your source space into a pair of n vectors, then

you get two "partial" gradients, each a 1byn matrix, and you get a 2 by 2 Hessian matrix, where each block is an nbyn matrix, i.e. 4 nbyn matrices of vector second derivatives

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Ok, I see. Thank you.

I.e. if R^n = V, the 1st derivative is a linear map VxV-->R, and the second derivative is a symmetric bilinear map (VxV)x(VxV)-->R.

So if you really want to break up your source space into a pair of n vectors, then

you get two "partial" gradients, each a 1byn matrix, and you get a 2 by 2 Hessian matrix, where each block is an nbyn matrix, i.e. 4 nbyn matrices of vector second derivatives

Regards

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