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

\(\sum\)

Series addition

\(\prod\)

Series multiplication

15.1.4. Functions

Symbol

Type

\(f(\cdot)\)

Function

\(\log(\cdot)\)

Natural logarithm

\(\exp(\cdot)\)

Exponential function

15.1.5. 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 \(\mathbf{x}\)

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)