Differences

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--- dot_product [2017/04/05 15:01] – 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 $\mathbb{R}^n$.
-\[ \color{blue}{\vec v\cdot\vec w=v_1w_1+v_2w_2+\dots+v_nw_n}.\]
-In other words, $\vec v\cdot \vec w$ is the [[row-column product]] $(\vec v)^T\vec w$ of the [[transpose]] of $\vec v$ with $\vec w$.
+The **dot product** of $\vec v$ and $\vec w$ is the number $\vec v\cdot \vec w$ given by
+\[ \color{red}{\vec v\cdot\vec w=v_1w_1+v_2w_2+\dots+v_nw_n}.\]