# Notation#

This section summarizes major notation used in the book.

## Numbers#

Notation

Meaning

Reference

$$\Nat$$

The set of natural numbers

$$\ZZ$$

The set of integers

$$\QQ$$

The set of rational numbers

$$\RR$$

The set of real numbers

Definition 2.1

$$\ERL$$

The extended real line $$[-\infty, \infty]$$

Definition 2.40

$$\CC$$

The set of complex numbers

$$\Re(x)$$

The real part of a complex number

$$\Im(x)$$

The imaginary part of a complex number

## Sets and Functions#

Notation

Meaning

Reference

$$\dom f$$

Domain of a function $$f$$

Definition 1.49

$$\range f$$

Range of a function $$f$$

Definition 1.51

$$\epi f$$

Epigraph of a function $$f$$

$$\supp f$$

Support of a function $$f$$

$$g \circ f$$

Composition of functions $$g$$ and $$f$$ with $$(g \circ f)(x) = g(f(x))$$

Definition 1.58

## Linear Algebra#

Notation

Meaning

$$\VV$$

A vector space (usually finite dimensional)

$$\EE$$

A normed vector space (usually finite dimensional and Euclidean)

$$\RR^n$$

$$n$$ dimensional Euclidean real vector space

$$\RR^{m \times n}$$

The space of $$m \times n$$ real matrices

$$\SS^{n}$$

The space of $$n \times n$$ symmetric real matrices

$$\NullSpace(A)$$

Null space of a matrix $$A$$

$$\ColSpace(A)$$

Column space of a matrix $$A$$

$$\RowSpace(A)$$

Row space of a matrix $$A$$

$$\Range(A)$$

Range of a set of vectors $$A$$

$$\Nullity(A)$$

Nullity of a an operator $$A$$

$$\Trace(A)$$

Trace of a matrix $$A$$

$$\Diag(A)$$

Diagonal of a matrix $$A$$

$$\supp(v)$$

Support of a vector $$v$$ (non-zero indices)

$$\bzero$$

The all zeros vector

$$\bone$$

The all ones vector

## Topology / Metric Spaces#

Notation

Meaning

$$\interior A$$

The interior of a set $$A$$

$$\closure A$$

The closure of a set $$A$$

$$\boundary A$$

The boundary of a set $$A$$

$$\diam A$$

The diam of a set $$A$$

$$\relint A$$

The relative interior of a set $$A$$

## Calculus#

Notation

Meaning

Reference

$$\lim_{x \to a} f(x)$$

Limit of $$f$$ as $$x$$ approaches $$a$$

Definition 2.64

$$x \to a^-$$

$$x$$ approaches $$a$$ from the left

Definition 2.65

$$x \to a^+$$

$$x$$ approaches $$a$$ from the right

Definition 2.65

$$f(a^-)$$

Left hand limit of $$f$$ at $$x=a$$

Definition 2.65

$$f(a^+)$$

Right hand limit of $$f$$ at $$x=a$$

Definition 2.65

$$f'$$

First derivative of $$f$$

Definition 2.78

$$f^{(1)}$$

1st derivative of $$f$$

Definition 2.81

$$f^{(n)}$$

n-th derivative of $$f$$

Definition 2.81

$$f^{(0)}$$

0-th derivative of $$f$$ ($$f^{(0)}=f$$)

Definition 2.81

$$f'_-(a)$$

Left hand derivative of $$f$$ at $$x=a$$

Definition 2.83

$$f'_+(a)$$

Right hand derivative of $$f$$ at $$x=a$$

Definition 2.83

$$\nabla f$$

Gradient of $$f$$

## Convex Analysis#

Notation

Meaning

$$\prox_f$$

The proximal operator for a function $$f$$