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Answer by greg for Rule chain matrix by vector

Take an ordinary scalar function $\phi(z)$ and its derivative$\phi'(z)=\frac{d\phi}{dz}$ and apply them element-wise to a vector argument, i.e. $$\eqalign{v &= X\beta,\quadf &=...

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Answer by Masacroso for Rule chain matrix by vector

You have that, as you wrote$$\partial[f(X\beta)]=\partial f(X\beta) X$$for $f:\Bbb R^n\to[0,\infty)$ and $X:\Bbb R^p\to\Bbb R^n$. Then $\partial f(X\beta)$ can be represented by the gradient $\nabla...

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Rule chain matrix by vector

Let $\boldsymbol{X}$ be a $n \times p$ matrix and $\boldsymbol{\beta}$ a $p-$dimensional vector. I'd like to calculate$$\frac{\partial f(\boldsymbol{X\beta})}{\partial\boldsymbol{\beta}}$$I...

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