# Not clear on how a simple vector subtraction was opened up to a summation.

As part of a derivation, I have the following derivation. I understand the whole thing, but I do not understand how the author went from the first line here, to the second line. Can someone please elucidate how they did that?

He basically seems to have "opened up" the $\mathbf{x} - \mathbf{x}_i$ term, but I am not clear how that translates to what is written in the second line.

Context: The formula comes from a derivation here

Thanks

• @Spacey I can't say much more about this without some more context (and even with more context, I don't know much about gaussian functions). All I can say is that the author probably moved the $\mathbf{x_i}$ inside the summation because that worked in the current derivation that they were working on. Since $\mathbf{x_i}$ does not depend on the index of summation it is perfectly fine to put it wherever works best for the proof, just as I can write $5\cdot(3+x)=(5\cdot3+5\cdot x)$. Commented May 17, 2017 at 15:53
• Wait...but $x_i$ does depend on the index of summation... Commented May 17, 2017 at 16:00