# 15.1. List of Main Symbols¶

The main symbols used in this book are listed below.

## 15.1.1. Numbers¶

Symbol

Type

$$x$$

Scalar

$$\mathbf{x}$$

Vector

$$\mathbf{X}$$

Matrix

$$\mathsf{X}$$

Tensor

## 15.1.2. Sets¶

Symbol

Type

$$\mathcal{X}$$

Set

$$\mathbb{R}$$

Real numbers

$$\mathbb{R}^n$$

Vectors of real numbers in $$n$$ dimensions

$$\mathbb{R}^{a \times b}$$

Matrix of real numbers with $$a$$ rows and $$b$$ columns

## 15.1.3. Operators¶

Symbol

Type

$$\mathbf{(\cdot)} ^\top$$

Vector or matrix transposition

$$\odot$$

Element-wise multiplication

$$\lvert\mathcal{X }\rvert$$

Cardinality (number of elements) of the set $$\mathcal{X}$$

$$\|\cdot\|_p$$

$$L_p$$ norm

$$\|\cdot\|$$

$$L_2$$ norm

$$\sum$$

$$\prod$$

Series multiplication

## 15.1.4. Functions¶

Symbol

Type

$$f(\cdot)$$

Function

$$\log(\cdot)$$

Natural logarithm

$$\exp(\cdot)$$

Exponential function

Symbol

Type

$$\frac{dy}{dx}$$

Derivative of $$y$$ with respect to $$x$$

$$\partial_{x} {y}$$

Partial derivative of $$y$$ with respect to $$x$$

$$\nabla_{\mathbf{x}} y$$

Gradient of $$y$$ with respect to $$\mathbf{x}$$

## 15.1.6. Probability and Statistics¶

Symbol

Type

$$\Pr(\cdot)$$

Probability distribution

$$z \sim \Pr$$

Random variable $$z$$ obeys the probability distribution $$\Pr$$

$$\Pr(x|y)$$

Conditional probability of $$x|y$$

$${\mathbf{E}}_{x} [f(x)]$$

Expectation of $$f$$ with respect to $$x$$

## 15.1.7. Complexity¶

Symbol

Type

$$\mathcal{O}$$

Big O notation

$$\mathcal{o}$$

Little o notation (grows much more slowly than)