What does the Cauchy-Schwarz inequality state for vectors u,v\mathbf{u}, \mathbf{v}u,v?
∣u⋅v∣≤∥u∥+∥v∥|\mathbf{u} \cdot \mathbf{v}| \leq \|\mathbf{u}\| + \|\mathbf{v}\|∣u⋅v∣≤∥u∥+∥v∥
∣u⋅v∣≤∥u∥⋅∥v∥|\mathbf{u} \cdot \mathbf{v}| \leq \|\mathbf{u}\| \cdot \|\mathbf{v}\|∣u⋅v∣≤∥u∥⋅∥v∥
u⋅v≥∥u∥⋅∥v∥\mathbf{u} \cdot \mathbf{v} \geq \|\mathbf{u}\| \cdot \|\mathbf{v}\|u⋅v≥∥u∥⋅∥v∥
∣u⋅v∣=∥u∥⋅∥v∥|\mathbf{u} \cdot \mathbf{v}| = \|\mathbf{u}\| \cdot \|\mathbf{v}\|∣u⋅v∣=∥u∥⋅∥v∥ always