Differences

This shows you the differences between two versions of the page.

--- dot_product [2017/04/05 15:02] – rupert
+++ dot_product [2017/04/05 15:04] (current) – rupert
@@ Line 1: / Line 1: @@
-Let $\def\m#1{\begin{bmatrix}#1\end{bmatrix}}\vec v=\m{v_1\\v_2\\\vdots\\v_n}$ and $\vec w=\m{w_1\\w_2\\\vdots\\w_n}$ be two (column) vectors in $\mathbb{R}^n$. The **dot product** of $\vec v$ and $\vec w$ is the real number $\vec v\cdot \vec w$ given by
+Let $\def\m#1{\left[\begin{smallmatrix}#1\end{smallmatrix}\right]}\vec v=\m{v_1\\v_2\\\vdots\\v_n}$ and $\vec w=\m{w_1\\w_2\\\vdots\\w_n}$ be two vectors in $\mathbb{R}^n$.
+The **dot product** of $\vec v$ and $\vec w$ is the number $\vec v\cdot \vec w$ given by
 \[ \color{red}{\vec v\cdot\vec w=v_1w_1+v_2w_2+\dots+v_nw_n}.\]