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arrow_back What is the dot product of u a column matrix and v a row matrix?

by Platinum
(103,030 points)
in Mathematics
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What is the dot product of u a column matrix and v a row matrix?

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Best answer

$$
\mathbf{u} \cdot \mathbf{v}=\mathbf{u v}=\mathbf{v}^{T} \mathbf{u}^{T}
$$

Example:

$$
\begin{aligned}
&\mathbf{u v}=\left[\begin{array}{lll}
1 & -3 & 5
\end{array}\right]\left[\begin{array}{l}
5 \\
4 \\
0
\end{array}\right]=-7 \\
&\mathbf{v}^{T} \mathbf{u}^{T}=\left[\begin{array}{lll}
5 & 4 & 0
\end{array}\right]\left[\begin{array}{r}
1 \\
-3 \\
5
\end{array}\right]=-7
\end{aligned}
$$

by Platinum
(103,030 points)
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