**Appendix A**

**Mathematical background**

In this appendix we give a brief review of some basic concepts from analysis and linear algebra. The treatment is by no means complete, and is meant mostly to set out our notation.

**A.1 Norms**

**A.1.1 Inner product, Euclidean norm, and angle**

The *standard inner product* on **R**^{n}, the set of real *n*-vectors, is given by

for *x, y* ∈ **R**^{n}. In this book we use the notation *x*^{T} *y*, instead of . The *Euclidean norm*, or *ℓ*_{2}-norm, of a vector *x* ∈ **R**^{n} is defined as

(A.1) |

The *Cauchy-Schwartz inequality* states that for any ...

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