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For the following proposition could someone perhaps explain to me moving from equation 45 to 46? I would be most grateful if you could do so with an example with simple matrices A and x.

enter image description here

Thanks again!

InvestingScientist
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    One can illustrate how it works by observing $n=3$ case. $\alpha = a_{11} x_1^2 + a_{12} x_1 x_2 + a_{13}x_1 x_3 + a_{21}x_2x_1 + a_{31}x_3x_1 + \text{ (some function without $x_1$})$, so $\partial_1 \alpha = 2 a_{11}x_1 + a_{12}x_2 + a_{13}x_3 + a_{21}x_2 + a_{31} x_3$. Write $2a_{11}x_1 = a_{11}x_1 + a_{11}x_1$ and proceed to the sigma notation. – dust05 May 29 '20 at 02:13
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    The key relation is $\frac{\partial x}{\partial x}=I$ where $I$ is the identity matrix; or in component form $\frac{\partial x_i}{\partial x_j}=\delta_{ij}$ – greg May 29 '20 at 02:56
  • Thank you both! – InvestingScientist May 29 '20 at 10:08
  • Can you please share the source of this picture? – Sachin Feb 23 '23 at 10:24

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