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

by Platinum
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What is the dot product of u a row matrix and v a row matrix?

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$$ \mathbf{u} \cdot \mathbf{v}=\mathbf{u v}^{T}=\mathbf{v u}^{T} $$ Example: $$ \begin{aligned} &\mathbf{u v}^{T}=\left[\begin{array}{lll} 1 & -3 & 5 \end{array}\right]\left[\begin{array}{l} 5 \\ 4 \\ 0 \end{array}\right]=-7 \\ &\mathbf{v u}^{T}=\left[\begin{array}{lll} 5 & 4 & 0 \end{array}\right]\left[\begin{array}{l} 1 \\ -3 \\ 5 \end{array}\right]=-7 \end{aligned} $$
by Platinum
(106,844 points)

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