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.