Row vector multiplication?

Given two row vectors, $(a, b, c )$, and $( x, y, z )$, does the operation of creating a new row vector in the format $$( ax, by, cz )$$ have a name?

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• Else, $$p=(a,b,c)\quad q=(x,y,z)$$ $$N=\sum_{i=1}^3p_iq_ie_i$$
$$N=diag(a)\times b$$
Could you explain what e is? – Šime Vidas Dec 2 '12 at 18:16
$e_i$ is (AFAIK) universal notation for a vector with $1$ at the $i^{th}$ location and $0$ everywhere else. So, $e_1 \in \mathbb{R}^3$ is $[1 \quad 0\quad 0]^T$. – Inquest Dec 2 '12 at 18:17