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I have the following statement in a text:

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I am not sure how the following expression was expanded to such. Where did the square root 2 come from, and how come we have an i and j iterator in the first term, but not in the second

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  • $\begingroup$ try to work with an example, say $x=(x_1,x_2,x_3)$, and $z=(z_1,z_2,z_3)$ $\endgroup$
    – Haitao Du
    Oct 8 '18 at 5:04
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Might be easier for you if it was written like that: $$ K(x,z) = (x^Tz + c)^2 = x^Tz \cdot z^Tx + 2x^Tz + c^2 $$ $$ = \sum_{i,j = 1}^n (x_iz_i)(x_jz_j) + \sum_{i=1}^n 2c(x_iz_i) + c^2 $$

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  • $\begingroup$ oh..right this is very naive my bad $\endgroup$
    – raaj
    Oct 8 '18 at 19:22

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