Harry Wang

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.

For inline mode, enclose the formula in $...$
For display mode (formulas will be centered and displayed in a separate line), enclose the formula in $$...$$

Symbol	Code	Symbol	Code
$y^{x}$	`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`

Symbol	Code	Symbol	Code
$\leq$	`\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`

Symbol	Code	Symbol	Code
$\alpha$	`\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:

Symbol	Typical Meaning
$a,b,c, \alpha,\beta,\gamma$	Scalars are lowercase
$\mathbf{x},\mathbf{y},\mathbf{z}$	Vectors are bold lowercase
$\mathbf{A},\mathbf{B},\mathbf{C}$	Matrices are bold uppercase
$\mathbf{x}^\top, \mathbf{A}^\top$	Transpose of a vector or matrix
$\mathbf{A}^{-1}$	Inverse of a matrix
$\langle \mathbf{x}, \mathbf{y}\rangle$	Inner product of $\mathbf{x}$ and $\mathbf{y}$
$\mathbf{x}^\top \mathbf{y}$	Dot product of $\mathbf{x}$ and $\mathbf{y}$
$B = (\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3)$	(Ordered) tuple
$\mathbf{B} = [\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3]$	Matrix of column vectors stacked horizontally
$\mathcal{B} = \{\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3\}$	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
$\mathcal{A}, \mathcal{C}$	Sets
$a \in \mathcal{A}$	$a$ is an element of set $\mathcal{A}$
$\emptyset$	Empty set
$\mathcal{A}\setminus \mathcal{B}$	$\mathcal{A}$ without $\mathcal{B}$ : the set of elements in $\mathcal{A}$ but not in $\mathcal{B}$
$D$	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 $m\times n$
$\mathbf{e}_i$	Standard canonical vector (where $i$ is the component that is $1$ )
$\dim$	Dimensionality of vector space
$\mathrm{rk}(\mathbf{A})$	Rank of matrix $\mathbf{A}$
$\mathrm{Im}(\Phi)$	Image of linear mapping $\Phi$
$\mathrm{ker}(\Phi)$	Kernel (null space) of a linear mapping $\Phi$
$\mathrm{span}[\mathbf{b}_1]$	Span (generating set) of $\mathbf{b}_1$
$\text{tr}(\mathbf{A})$	Trace of $\mathbf{A}$
$\det(\mathbf{A})$	Determinant of $\mathbf{A}$
$\\| \cdot \\|$	Absolute value or determinant (depending on context)
$\\|\\| \cdot \\|\\|$	Norm; Euclidean, unless specified
$\lambda$	Eigenvalue or Lagrange multiplier
$E_\lambda$	Eigenspace corresponding to eigenvalue $\lambda$
$\mathbf{x} \perp \mathbf{y}$	Vectors $\mathbf{x}$ and $\mathbf{y}$ 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 $x_n$ : $x_1 \cdot\dotsc \cdot x_N$
$\boldsymbol{\theta}$	Parameter vector
$\frac{\partial f}{\partial x}$	Partial derivative of $f$ with respect to $x$
$\frac{\mathrm{d} f}{\mathrm{d} x}$	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)
$\mathfrak{L}$	Lagrangian
$\mathcal{L}$	Negative log-likelihood
$\binom{n}{k}$	Binomial coefficient, $n$ choose $k$
$\mathbb{V}_X[\mathbf{x}]$	Variance of $\mathbf{x}$ with respect to the random variable $X$
$\mathbb{E}_X[\mathbf{x}]$	Expectation of $\mathbf{x}$ with respect to the random variable $X$
$\operatorname{Cov}_{X,Y}[\mathbf{x}, \mathbf{y}]$	Covariance between $\mathbf{x}$ and $\mathbf{y}$
$X \perp\kern-5pt\perp Y \vert Z$	$X$ is conditionally independent of $Y$ given $Z$
$X\sim p$	Random variable $X$ is distributed according to $p$
$\mathcal{N}\big(\boldsymbol{\mu},\boldsymbol{\Sigma}\big)$	Gaussian distribution with mean $\boldsymbol{\mu}$ and covariance $\boldsymbol{\Sigma}$
$\text{Ber}(\mu)$	Bernoulli distribution with parameter $\mu$
$\text{Bin}(N, \mu)$	Binomial distribution with parameters $N, \mu$
$\text{Beta}(\alpha, \beta)$	Beta distribution with parameters $\alpha, \beta$

A more complete LaTex cheatsheet can be found here.