arrow_back What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?

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What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?

The dot product of $\mathbf{u}$  a column matrix and $\mathbf{v}$ a column matrix is:

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

Example:

\begin{aligned} &\mathbf{u}^{T} \mathbf{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}=\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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