## Prove the Cauchy-Schwarz Inequality

## Problem 355

Let $\mathbf{a}, \mathbf{b}$ be vectors in $\R^n$.

Prove the **Cauchy-Schwarz inequality**:

\[|\mathbf{a}\cdot \mathbf{b}|\leq \|\mathbf{a}\|\,\|\mathbf{b}\|.\]

Let $\mathbf{a}, \mathbf{b}$ be vectors in $\R^n$.

Prove the **Cauchy-Schwarz inequality**:

\[|\mathbf{a}\cdot \mathbf{b}|\leq \|\mathbf{a}\|\,\|\mathbf{b}\|.\]