Dive into Deep Learning
Table Of Contents
Dive into Deep Learning
Table Of Contents

14.1. List of Main Symbols

The main symbols used in this book are listed below.

14.1.1. Numbers

Symbol

Type

\(x\)

Scalar

\(\mathbf{x}\)

Vector

\(\mathbf{X}\)

Matrix

\(\mathsf{X}\)

Tensor

14.1.2. 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

14.1.3. 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

\(\sum\)

Series addition

\(\prod\)

Series multiplication

14.1.4. Functions

Symbol

Type

\(f(\cdot)\)

Function

\(\log(\cdot)\)

Natural logarithm

\(\exp(\cdot)\)

Exponential function

14.1.5. Derivatives and Gradients

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 \(\mathbf{x}\)

14.1.6. 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 \(x\)

14.1.7. Complexity

Symbol

Type

\(\mathcal{O}\)

Big O notation

\(\mathcal{o}\)

Little o notation (grows much more slowly than)