February 9, 2022

LaTex Cheatsheet

This is a simple LaTex Cheatsheet for writing math symbols and formulas in Jupyter Notebook, which uses MathJax to render LaTex inside the Markdown cells.

\(y^{x}\) y^{x} \(y_{x}\) y_{x}
\(\frac{x}{y}\) \frac{x}{y} \(\sum_{k=1}^n\) \sum_{k=1}^n
\(\sqrt[n]{x}\) \sqrt[n]{x} \(\prod_{k=1}^n\) \prod_{k=1}^n
\(\leq\) \leq \(\geq\) \geq
\(\neq\) \neq \(\approx\) \approx
\(\times\) \times \(\div\) \div
\(\pm\) \pm \(\cdot\) \cdot
\(x^{\circ}\) x^{\circ} \(\circ\) \circ
\(x^\prime\) x^\prime \(\cdots\) \cdots
\(\infty\) \infty \(\neg\) \neg
\(\wedge\) \wedge \(\vee\) \vee
\(\supset\) \supset \(\forall\) \forall
\(\in\) \in \(\rightarrow\) \rightarrow
\(\subset\) \subset \(\exists\) \exists
\(\notin\) \notin \(\Rightarrow\) \Rightarrow
\(\cup\) \cup \(\cap\) \cap
\(\mid\) \mid \(\Leftrightarrow\) \Leftrightarrow
\(\dot a\) \dot a \(\hat a\) \hat a
\(\bar a\) \bar a \(\tilde a\) \tilde a
\(\alpha\) \alpha \(\beta\) \beta
\(\gamma\) \gamma \(\delta\) \delta
\(\epsilon\) \epsilon \(\zeta\) \zeta
\(\eta\) \eta \(\varepsilon\) \varepsilon
\(\theta\) \theta \(\iota\) \iota
\(\kappa\) \kappa \(\vartheta\) \vartheta
\(\pi\) \pi \(\rho\) \rho
\(\sigma\) \sigma \(\tau\) \tau
\(\upsilon\) \upsilon \(\phi\) \phi
\(\chi\) \chi \(\psi\) \psi
\(\omega\) \omega \(\Gamma\) \Gamma
\(\Delta\) \Delta \(\Theta\) \Theta
\(\Lambda\) \Lambda \(\Xi\) \Xi
\(\Pi\) \Pi \(\Sigma\) \Sigma
\(\Upsilon\) \Upsilon \(\Phi\) \Phi
\(\Psi\) \Psi \(\Omega\) \Omega

I also created the list of symbols table used in the Mathematics for Machine Learning book, which is a great LaTex reference and can be accessed at:

$ \renewcommand{\vec}[1]{\mathbf{#1}} % vector bf: boldface \newcommand{\mat}[1]{\mathbf{#1}} % matrix \renewcommand{\T}{^\top} % transpose \newcommand{\inv}{^{-1}} % inverse \newcommand{\set}[1]{\mathcal{#1}} % set cal: calligraphic letters \renewcommand{\dim}{\mathrm{dim}} % dimension, rm: roman typestyle \newcommand{\rank}{\mathrm{rk}} % rank \newcommand{\determ}[1]{\mathrm{det}(#1)} % determinant \renewcommand{\d}{\mathrm{d}} \newcommand{\id}{\mathrm{id}} % identity mapping \newcommand{\kernel}{\mathrm{ker}} % kernel/nullspace \newcommand{\img}{\mathrm{Im}} % image \newcommand{\idx}[1]{(#1)} \newcommand{\genset}[1]{\mathrm{span}[#1]} % generating set \newcommand{\tensor}[1]{\mathbb{#1}} % tensor \newcommand{\tr}{\text{tr}} % trace \newcommand{\pdiffF}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\diffF}[2]{\frac{\d #1}{\d #2}} \newcommand{\lag}{\mathfrak{L}} % lagrangian \newcommand{\lik}{\mathcal{L}} % likelihood \newcommand{\var}{\mathbb{V}} % variance \newcommand{\E}{\mathbb{E}} % expectation \DeclareMathOperator{\cov}{Cov} % covariance \newcommand\ci{\perp\kern-5pt \perp} % conditional independence \newcommand\given{\vert} % given % Gaussian distribution \newcommand{\gauss}[2]{\mathcal{N}\big(#1,#2\big)} % other distributions \newcommand{\Ber}{\text{Ber}} \newcommand{\Bin}{\text{Bin}} \newcommand{\Beta}{\text{Beta}} $

Symbol Typical Meaning
$a,b,c, \alpha,\beta,\gamma$ Scalars are lowercase
$\vec x,\vec y,\vec z$ Vectors are bold lowercase
$\mat A,\mat B,\mat C$ Matrices are bold uppercase
$\vec x \T , \mat A \T$ Transpose of a vector or matrix
$\mat A\inv$ Inverse of a matrix
$\langle \vec x, \vec y\rangle$ Inner product of $\vec x$ and $\vec y$
$\vec x \T \vec y$ Dot product of $\vec x$ and $\vec y$
$B = (\vec b_1, \vec b_2, \vec b_3)$ (Ordered) tuple
$\mat B = [\vec b_1, \vec b_2, \vec b_3]$ Matrix of column vectors stacked horizontally
$\set B = {\vec b_1, \vec b_2, \vec b_3}$ Set of vectors (unordered)
$\mathbb Z,\mathbb N$ Integers and natural numbers, respectively
$\mathbb R,\mathbb C$ Real and complex numbers, respectively
$\mathbb R^n$ $n$-dimensional vector space of real numbers
$\forall x$ Universal quantifier: for all $x$
$\exists x$ Existential quantifier: there exists $x$
$a := b$ $a$ is defined as $b$
$a =:b$ $b$ is defined as $a$
$a\propto b$ $a$ is proportional to $b$, i.e., $a =\text{constant}\cdot b$
$g\circ f$ Function composition: $g$ after $f$
$\iff$ If and only if
$\implies$ Implies
$\set A, \set C$ Sets
$a \in \set A$ $a$ is an element of set $\set A$
$\emptyset$ Empty set
$\set A\setminus \set B$ $\set A$ without $\set B$: the set of elements in $\set A$ but not in $\set B$
$D$ Number of dimensions; indexed by $d=1,\dots,D$
$N$ Number of data points; indexed by $n=1,\dots,N$
$\mathbf{I}_m$ Identity matrix of size $m\times m$
$\mathbf{0}_{m,n}$ Matrix of zeros of size $m\times n$
$\mathbf{1}_{m,n}$ Matrix of ones of size $m\times n$
$\vec e_i$ Standard canonical vector (where $i$ is the component that is $1$)
$\dim$ Dimensionality of vector space
$\rank(\mat A)$ Rank of matrix $\mat A$
$\img(\Phi)$ Image of linear mapping $\Phi$
$\kernel(\Phi)$ Kernel (null space) of a linear mapping $\Phi$
$\genset{\vec b_1}$ Span (generating set) of $\vec b_1$
$\tr(\mat A)$ Trace of $\mat A$
$\det(\mat A)$ Determinant of $\mat A$
$| \cdot |$ Absolute value or determinant (depending on context)
$|| {\cdot} ||$ Norm; Euclidean, unless specified
$\lambda$ Eigenvalue or Lagrange multiplier
$E_\lambda$ Eigenspace corresponding to eigenvalue $\lambda$
$\vec x \perp \vec y$ Vectors $\vec x$ and $\vec y$ are orthogonal
$V$ Vector space
$V^\perp$ Orthogonal complement of vector space $V$
$\sum_{n=1}^N x_n$ Sum of the $x_n$: $x_1 + \dotsc + x_N$
$\prod_{n=1}^N x_n$ Product of the $x_n$: $x_1 \cdot\dotsc \cdot x_N$
$\vec \theta$ Parameter vector
$\pdiffF{f}{x}$ Partial derivative of $f$ with respect to $x$
$\diffF{f}{x}$ Total derivative of $f$ with respect to $x$
$\nabla $ Gradient
$f_* = \min_x f(x)$ The smallest function value of $f$
$x_* \in \arg\min_x f(x)$ The value $x_*$ that minimizes $f$ (note: $\arg\min$ returns a set of values)
$\lag$ Lagrangian
$\lik$ Negative log-likelihood
$\binom{n}{k}$ Binomial coefficient, $n$ choose $k$
$\var_X[\vec x]$ Variance of $\vec x$ with respect to the random variable $X$
$\E_X[\vec x]$ Expectation of $\vec x$ with respect to the random variable $X$
$\cov_{X,Y}[\vec x, \vec y]$ Covariance between $\vec x$ and $\vec y$.
$X \ci Y \given Z$ $X$ is conditionally independent of $Y$ given $Z$
$X\sim p$ Random variable $X$ is distributed according to $p$
$\gauss{\mat \mu}{\mat \Sigma}$ Gaussian distribution with mean $\vec \mu$ and covariance $\mat \Sigma$
$\Ber(\mu)$ Bernoulli distribution with parameter $\mu$
$\Bin(N, \mu)$ Binomial distribution with parameters $N, \mu$
$\Beta(\alpha, \beta)$ Beta distribution with parameters $\alpha, \beta$

A more complete LaTex cheatsheet can be found here.

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