Dot Product Operator is Commutative/Proof 1
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Theorem
- $\mathbf u \cdot \mathbf v = \mathbf v \cdot \mathbf u$
Proof
| \(\ds \mathbf u \cdot \mathbf v\) | \(=\) | \(\ds \sum_{i \mathop = 1}^n u_i v_i\) | Definition of Dot Product | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sum_{i \mathop = 1}^n v_i u_i\) | Real Multiplication is Commutative | |||||||||||
| \(\ds \) | \(=\) | \(\ds \mathbf v \cdot \mathbf u\) | Definition of Dot Product |
$\blacksquare$