Cauchy-Schwarz

• Very useful in proofs to derive upper bounds, e.g., when analyzing the error or the convergence rate of a numerical algorithm

$$|x^{T}y|\le \Vert x{\Vert }_2\Vert y{\Vert }_2$$

• Exercise: you can prove the triangle inequality using CS:

$$\Vert x+y{\Vert }_2\le \Vert x{\Vert }_2+\Vert y{\Vert }_2$$

• Dot product, Vector norms