Deep Learning Notation

Numerical Objects

Symbol	Meaning	LaTeX Notation
$x$	A scalar	$x$
$X$	A vector	$X$
$\mathbf{X}$	A matrix	$\mathbf{X}$
$\mathsf{X}$	A general tensor	$\mathsf{X}$
$\mathbf{I}$	The identity matrix	$\mathbf{I}$
$x_{ij}$, $x_{i,j}$, $[X]{ij}$, $[X]{i,j}$	The element of matrix $\mathbf{X}$ at row $𝑖$ and column $𝑗$	$x_{ij}$, $x_{i,j}$, $[X]_{ij}$, $[X]_{i,j}$

Set Theory

Symbol	Meaning	LaTeX Notation
$\mathcal{X}$	A set	$\mathcal{X}$
$\mathbb{Z}$	The set of integers	$\mathbb{Z}$
$\mathbb{Z}^+$	The set of positive integers	$\mathbb{Z}^+$
$\mathbb{R}$	The set of real numbers	$\mathsf{X}$
$\mathbb{R}^n$	the set of 𝑛-dimensional vectors of real numbers	$\mathbb{R}^n$
$\mathbb{R}^{a\times b}$	The set of matrices of real numbers with $𝑎$ rows and $𝑏$ columns	$\mathbb{R}^{a\times b}$
$\lvert\mathcal{X}\rvert$	Cardinality (number of elements) of set $\mathcal{X}$	$\lvert\mathcal{X}\rvert$
$\mathcal{A}\cup\mathcal{B}$	Union of sets A and B	$\mathcal{A}\cup\mathcal{B}$
$\mathcal{A}\cap\mathcal{B}$	Intersection of sets A and B	$\mathcal{A}\cap\mathcal{B}$
$\mathcal{A}\setminus \mathcal{B}$	Set subtraction of B from A	$\mathcal{A}\setminus \mathcal{B}$