Math macro command for latex support in markdown

command	visualization	comment
`a`	$a$	A scalar
`\va`	$a$	A vector, additionally $0, 1, μ, ν, θ$ for `\vzero, \vone, \vmu, \vnu, \vtheta`
`\mA`	$A$	A matrix
`\tA`	$A$	A tensor
`\mI_n`	$I_{n}$	Identity matrix with $n$ rows and $n$ columns
`\mI`	$I$	Identity matrix with dimensionality implied by context
`\ve^{(i)}`	$e^{(i)}$	Standard basis vector $[0, \dots, 0, 1, 0, \dots, 0]$ with a 1 at position $i$
`\text{diag}(\va)`	$diag (a)$	A square, diagonal matrix with diagonal entries given by $a$
`\ra`	$a$	A scalar-valued random variable
`\rva`	$a$	A vector-valued random variables
`\rmA`	$A$	A matrix-valued random varialbes

Command	Visualization	Comment
`\sA`	$A$	A set Note: the command covers `sA` to `sZ` but don't no `sE` since it's expectation
`\R`	$R$	The set of real numbers
`{0, 1}`	$0, 1$	The set containing 0 and 1
`{0, 1, \dots, n}`	$0, 1, \dots, n$	The set of all integers between $0$ and $n$
`[a, b]`	$[a, b]$	The real interval including $a$ and $b$
`(a, b]`	$(a, b]$	The real interval excluding $a$ but including $b$
`\sA \backslash \sB`	$A ∖ B$	Set subtraction, i.e., the set containing the elements of $A$ not in $B$
`\gG`	$G$	A graph

Command	Visualization	Comment
`\eva_i`	$a_{i}$	Element $i$ of vector $a$ , with indexing starting at 1
`\eva_{-i}`	$a_{- i}$	All elements of vector $a$ except for element $i$
`\emA_{i,j}`	$A_{i, j}$	Element $i, j$ of matrix $A$
`\mA_{i, :}`	$A_{i, :}$	Row $i$ of matrix $A$
`\mA_{:, i}`	$A_{:, i}$	Column $i$ of matrix $A$
`\etA_{i, j, k}`	$A_{i, j, k}$	Element $(i, j, k)$ of a 3-D tensor $A$
`\tA_{:, :, i}`	$A_{:, :, i}$	2-D slice of a 3-D tensor
`\erva_i`	$a_{i}$	Element $i$ of the random vector $a$

Command	Visualization	Comment
`\mA^\top`	$A^{⊤}$	Transpose of matrix $A$
`\mA^+`	$A^{+}$	Moore-Penrose pseudoinverse of $A$
`\mA \odot \mB`	$A ⊙ B$	Element-wise (Hadamard) product of $A$ and $B$
`\mathrm{det}(\mA)`	$\det (A)$	Determinant of $A$
`\sign(x)`	$sign (x)$	Sign of a variable $x$
`\Tr \mA`	$Tr (A)$	Trace of a matrix A

Command	Visualization	Comment
`\diff y / \diff x`	$d y / d x$	Derivative of $y$ with respect to $x$
`\frac{\partial y}{\partial x}`	$\frac{\partial y}{\partial x}$	Partial derivative of $y$ with respect to $x$
`\nabla_\vx y`	$\nabla_{x} y$	Gradient of $y$ with respect to $x$
`\nabla_\mX y`	$\nabla_{X} y$	Matrix derivatives of $y$ with respect to $X$
`\nabla_\tX y`	$\nabla_{X} y$	Tensor containing derivatives of $y$ with respect to $X$
`\frac{\partial f}{\partial \vx}`	$\frac{\partial f}{\partial x}$	Jacobian matrix $J \in R^{m \times n}$ of $f : R^{n} \to R^{m}$
`\nabla_\vx^2 f(\vx)\text{ or }\mH(f)(\vx)`	$\nabla_{x}^{2} f (x) or H (f) (x)$	The Hessian matrix of $f$ at input point $x$
`\int f(\vx) d\vx`	$\int f (x) d x$	Definite integral over the entire domain of $x$
`\int_\sS f(\vx) d\vx`	$\int_{S} f (x) d x$	Definite integral with respect to $x$ over the set $S$

Command	Visualization	Comment
`\ra \bot \rb`	$a ⊥ b$	The random variables $a$ and $b$ are independent
`\ra \bot \rb \mid \rc`	$a ⊥ b ∣ c$	They are conditionally independent given $c$
`P(\ra)`	$P (a)$	A probability distribution over a discrete variable
`p(\ra)`	$p (a)$	A probability distribution over a continuous variable, or a variable of unspecified type
`\ra \sim P`	$a \sim P$	Random variable $a$ has distribution $P$
`\E_{\rx \sim P} [ f(x) ] \text{ or } \E f(x)`	$E_{x \sim P} [f (x)] or E f (x)$	Expectation of $f (x)$ with respect to $P (x)$
`\Var(f(x))`	$Var (f (x))$	Variance of $f (x)$ under $P (x)$
`\Cov(f(x), g(x))`	$Cov (f (x), g (x))$	Covariance of $f (x)$ and $g (x)$ under $P (x)$
`H(\rx)`	$H (x)$	Shannon entropy of the random variable $x$
`\KL(P \Vert Q)`	$D_{KL} (P ‖ Q)$	Kullback-Leibler divergence of $P$ and $Q$
`\mathcal{N}(\vx ; \vmu , \mSigma)`	$N (x; μ, Σ)$	Gaussian distribution over $x$ with mean $μ$ and covariance $Σ$

Command	Visualization	Comment
`f: \sA \rightarrow \sB`	$f : A \to B$	The function $f$ with domain $A$ and range $B$
`f \circ g`	$f \circ g$	Composition of the functions $f$ and $g$
`f(\vx ; \vtheta)`	$f (x; θ)$	A function of $x$ parametrized by $θ$ . Sometimes written as $f (x)$ to simplify notation
`\log x`	$\log x$	Natural logarithm of $x$
`\sigma(x)`	$σ (x)$	Logistic sigmoid, $\frac{1}{1 + \exp (- x)}$
`\zeta(x)`	$ζ (x)$	Softplus, $\log (1 + \exp (x))$
`\Vert \vx \Vert_p`	$‖ x ‖_{p}$	$L^{p}$ norm of $x$
`\Vert \vx \Vert`	$‖ x ‖$	$L^{2}$ norm of $x$
`x^+`	$x^{+}$	Positive part of $x$ , i.e., $max (0, x)$
`\bm{1}_\mathrm{condition}`	$1_{condition}$	Is 1 if the condition is true, 0 otherwise

Command	Visualization	Comment
`\bm{#1}`	$x$	Bold symbol, e.g., $x$
`\sign`	$sign$	operator, Sign , $sign$
`\Tr`	$Tr$	operator Trace, $Tr$
`\E`	$E$	Expectation, $E$
`\KL`	$D_{KL}$	Kullback-Leibler divergence, $D_{KL}$
`\NormalDist`	$N$	Gaussian distribution, $N$
`\diag`	$diag$	Diagonal matrix, $diag$
`\Ls`	$L$	Loss function, $L$
`\R`	$R$	Real number set, $R$
`\emp`	$\tilde{p}$	Empirical distribution, $\tilde{p}$
`\lr`	$α$	Learning rate, $α$
`\reg`	$λ$	Regularization coefficient, $λ$
`\rect`	$rectifier$	Rectifier activation, $rectifier$
`\softmax`	$softmax$	Softmax function, $softmax$
`\sigmoid`	$σ$	Sigmoid function, $σ$
`\softplus`	$ζ$	Softplus function, $ζ$
`\Var`	$Var$	Variance, $Var$
`\standarderror`	$SE$	Standard error, $SE$
`\Cov`	$Cov$	Covariance, $Cov$
`\tran`	$^{⊤}$	Transpose operator, $^{⊤}$
`\inv`	$^{- 1}$	Inverse operator, $^{- 1}$
`\diff`	$d$	Differential operator, $d$

Reference

Ian Goodfellow's ML book: https://github.com/goodfeli/dlbook_notation/blob/master/notation_example.pdf
MathJax: https://docs.mathjax.org/en/latest/input/tex/macros.html