Notation

Expression	Description
\(\mathscr{C}\)	Set of the complex numbers
\(\mathscr{N}\)	Set of the natural numbers
\(\mathscr{N}_0\)	Set of the natural numbers including zero
\(\mathscr{Q}\)	Set of the rational numbers
\(\mathscr{R}\)	Set of the real numbers

Linear Algebra

Expression	Description
\(\dim S\)	Dimension of \(S\)
\(N(A)\)	Null space of \(A\)
\(R(A)\)	Range of \(A\)
\(\text{rk}A\)	Rank of \(A\)
\(I_n\)	\(n\)-by-\(n\) identity matrix

Real Analysis and Topology

Expression	Description
\(\text{int}(S)\)	Interior of \(S\)
\(\text{cl}(S)\)	Closure of \(S\)
\(\partial S\)	Boundary of \(S\)
\(\varphi : X \rightrightarrows Y\)	Correspondence \(\varphi\) from \(X\) to \(Y\)
\(\text{co}S\)	Convex hull of \(S\)

Statistics

Expression	Description
\(a \perp b\)	The random variables \(a\) and \(b\) are independent
\(a \perp b \mid c\)	They are conditionally independent given \(c\)
\(P(a)\)	A probability distribution over a discrete variable
\(p(a)\)	A probability distribution over a continuous variable, or over a variable whose type has not been specified
\(a \sim P\)	Random variable \(a\) has distribution \(P\)
\(E_{\mathrm{x}\sim P} [f(x)]\) or \(E[f(x)]\)	Expectation of \(f(x)\) with respect to \(P(\mathrm{x})\)
\(\text{Var}(f(x))\)	Variance of \(f(x)\) under \(P(\mathrm{x})\)
\(\text{Cov}(f(x), g(x))\)	Covariance of \(f(x)\) and \(g(x)\) under \(P(\mathrm{x})\)
\(\mathscr{N}(\mathbf{x}; \mathbf{\mu}, \mathbf{\Sigma})\)	Gaussian distribution over \(\mathbf{x}\) with mean \(\mathbf{\mu}\) and covariance \(\mathbf{\Sigma}\)
\(\mu_n'\)	\(n\)th (raw) moment of a distribution
\(\mu_n\)	\(n\)th central moment of a distribution
\(X_n \overset{d}{\longrightarrow}X\)	\(X_n\) converges in distribution to \(X\)
\(X_n \overset{p}{\longrightarrow}X\)	\(X_n\) converges in probability to \(X\)
\(X_n \overset{L^r}{\longrightarrow}X\)	\(X_n\) converges in the \(r\)th mean to \(X\)
\(X_n \overset{L^2}{\longrightarrow}X\)	\(X_n\) converges in quadratic mean to \(X\)