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

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)