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

12.1. List of Main Symbols

The main symbols used in this book are listed below.

12.1.1. Numbers

\(x\) Scalar
\(\boldsymbol{x}\) Vector
\(\boldsymbol{X}\) Matrix
\(\mathsf{X}\) Tensor

12.1.2. Sets

\(\mathcal{X}\) Set
\(\mathbb{R}\) Real number set
\(\mathbb{R}^n\) Real number vector set of \(n\) dimension
\(\mathbb{R}^{x \times y}\) Real number matrix set with \(x\) rows and \(y\) columns

12.1.3. Operators

\(\boldsymbol{(\cdot)}^\top\) Vector or matrix transposition
\(\odot\) Multiply by element
\(\lvert\mathcal{X}\rvert\) Number of elements in the set \(\mathcal{X}\)
\(\|\cdot\|_p\) \(L_p\) norm
\(\|\cdot\|\) \(L_2\) norm
\(\sum\) Continuous addition
\(\prod\) Continuous multiplication

12.1.4. Functions

\(f(\cdot)\) Function
\(\log(\cdot)\) Natural logarithmic function
\(\exp(\cdot)\) Exponential function

12.1.5. Derivatives and Gradients

\(\frac{dy}{dx}\) Derivative of \(y\) with respect to \(x\)
:math:`frac{partial y}{partial
x}`
Partial derivative of \(y\) with respect to \(x\)
\(\nabla_{\cdot} y\) Gradient of \(y\) with respect to \(\cdot\)

12.1.6. Probability and Statistics

\(\mathbb{P}(\cdot)\) Probability distribution
\(\cdot \sim \mathbb{P}\) Random variable \(\cdot\) obeys the probability distribution \(\mathbb{P}\)
\(\mathbb{P}(\cdot \mid\cdot )\) Conditional probability
\(\mathbb{E}_{\cdot}\left(f( \cdot)\right)\) Expectation of \(f(\cdot)\) with respect to \(\cdot\)

12.1.7. Complexity

\(\mathcal{O}\) Big O notation