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

16.1. List of Main Symbols

The main symbols used in this book are listed below.

16.1.1. Numbers

Symbol Type
\(x\) Scalar
\(\mathbf{x}\) Vector
\(\mathbf{X}\) Matrix
\(\mathsf{X}\) Tensor

16.1.2. 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

16.1.3. 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

16.1.4. Functions

Symbol Type
\(f(\cdot)\) Function
\(\log(\cdot)\) Natural logarithm
\(\exp(\cdot)\) Exponential function

16.1.5. 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 \(\mathbf{x}\)

16.1.6. 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 \(x\)

16.1.7. Complexity

Symbol Type
\(\mathcal{O}\) Big O notation
\(\mathcal{o}\) Little o notation (grows much more slowly than)

16.1.8. Scan the QR Code to Discuss