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What is the dot product of u a column matrix and v a row matrix?
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$$\mathbf{u} \cdot \mathbf{v}=\mathbf{u v}=\mathbf{v}^{T} \mathbf{u}^{T}$$

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}

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