| \(a\), \(b\) |
(known) variable or element of a set |
|
| \(c\) |
constant |
|
| \(e\) |
mathematical constant \(e\) (Euler’s number) |
|
| \(\pi\) |
mathematical constant \(\pi\) |
\pi |
| \(\varepsilon\) |
small positive infinitesimal quantity |
\varepsilon |
| \(i\) |
general integer; subscript or superscript; imaginary unit |
|
| \(j\), \(k\), \(l\) |
general integer; subscript or superscript |
|
| \(n\), \(m\) |
general natural number; total number |
|
| \(p\) |
general prime number; general probability |
|
| \(q\) |
general prime number |
|
| \(x\), \(y\) |
(unknown) variable or element of a set; coordinate |
|
| \(z\), \(w\) |
general complex number; coordinate |
|
| \(\vert x \vert\), \(\vert z \vert\) |
absolute value |
|
| \(\bar{z}\) |
complex conjugate |
\bar{z} |
| \(\Re(z)\); \(\operatorname{Re}(z)\) |
real part |
\Re{z} |
| \(\Im(z)\); \(\operatorname{Im}(z)\) |
imaginary part |
\Im(z) |
| \(\mathcal{E}\) |
experiment |
\mathcal{E} |
| \(A\), \(B\) |
(known) set; event |
|
| \(S\), \(\Omega\) |
set; class of sets; sample space |
|
| \(U\) |
universal set |
|
| \(A^\complement\); \(\overline{A}\); \(\complement_U A\) |
complement of set |
A^\complement |
| \(\varnothing\) |
empty set |
\varnothing |
| \(X\), \(Y\) |
(unknown) set; random variable |
|
| \(\mathcal{X}\), \(\mathcal{Y}\) |
set with special structure, space |
\mathcal{X} |
| \(\mathcal{P}(S)\); \(2^S\) |
power set |
\mathcal{P}(S) |
| \(\vert S \vert\); \(\operatorname{Card}(S)\) |
cardinality of set |
|
| \(\aleph_0\) |
cardinality of natural numbers (Aleph-naught) |
\aleph_0 |
| \(\mathfrak{c}\) |
cardinality of continuum |
\mathfrak{c} |
| \(\mathbb{N}\) |
set of natural numbers |
\mathbb{N} |
| \(\mathbb{Z}^+\) |
set of positive integers |
\mathbb{Z}^+ |
| \(\mathbb{Z}\) |
set of integers |
\mathbb{Z} |
| \(\mathbb{Q}\) |
set of rational numbers |
\mathbb{Q} |
| \(\mathbb{R}\) |
set of real numbers |
\mathbb{R} |
| \(\mathbb{R}^n\) |
\(n\)-dimensional real coordinate space |
\mathbb{R}^n |
| \(\mathbb{C}\) |
set of complex numbers |
\mathbb{C} |
| \(\mathbb{C}^n\) |
\(n\)-dimensional complex coordinate space |
\mathbb{C}^n |
| \(\mathbf{A}\), \(\mathbf{B}\), \(\mathbf{X}\), \(\mathbf{Y}\) |
matrix |
\mathbf{A} |
| \(\boldsymbol{a}\), \(\boldsymbol{b}\), \(\boldsymbol{x}\), \(\boldsymbol{y}\) |
vector |
\boldsymbol{a} |
| \(\boldsymbol{e}\), \(\boldsymbol{i}\), \(\boldsymbol{j}\), \(\boldsymbol{k}\) |
unit vector |
|
| \(\boldsymbol{v}\) |
eigenvector |
|
| \(\lambda\) |
eigenvalue |
\lambda |
| \(\vert\vert \boldsymbol{a} \vert\vert\), \(\vert\vert \mathbf{A} \vert\vert\) |
norm |
|
| \(\langle \boldsymbol{a},\boldsymbol{b} \rangle\) |
inner product of vectors |
|
| \(\mathbf{I}_n\) |
identity matrix of size \(n\) |
|
| \(\operatorname{diag}(a_1,\dots,a_n)\) |
diagonal matrix of size \(n\) |
|
| \(\delta_{ij}\) |
Kronecker delta |
\delta_{ij} |
| \(\mathbf{A}^{\rm T}\) |
transpose of matrix |
\mathbf{A}^{\rm T} |
| \(\mathbf{A}^{-1}\) |
inverse of matrix |
\mathbf{A}^{-1} |
| \(\operatorname{rank}(\mathbf{A})\) |
rank of matrix |
|
| \(\det(\mathbf{A})\) |
determinant of matrix |
\det(\mathbf{A}) |
| \(f\), \(g\), \(h\) |
function or mapping |
|
| \(\varphi\) |
function or mapping with special property |
\varphi |
| \(\delta\) |
Dirac delta function |
\delta |
| \(\eta\) |
Dedekind eta function |
\eta |
| \(\psi\), \(\Psi\) |
wave function |
\psi |
| \(\wp\) |
Weierstrass’s elliptic function |
\wp |
| \(\operatorname{negl}(x)\) |
negligible function |
|
| \(\min(S)\) |
minimum |
\min(S) |
| \(\max(S)\) |
maximum |
\max(S) |
| \(\sup(S)\) |
supremum |
\sup(S) |
| \(\inf(S)\) |
infimum |
\inf(S) |
| \(\lim(f(x))\); \(\lim(a_n)\) |
limit |
\lim(f(x)) |
| \(d{x}\) |
differential operator |
|
| \(\partial{x}\) |
partial differential operator |
\partial{x} |
| \(\Delta\) |
forward difference; Laplace operator |
\Delta |
| \(\nabla\) |
backward difference; gradient |
\nabla |
| \(e^{x}\); \(\exp(x)\) |
exponential function |
|
| \(\ln(x)\) |
natural logarithm |
\ln(x) |
| \(\log(x)\) |
logarithm |
\log(x) |
| \(\mathcal{A}\) |
algorithm |
\mathcal{A} |
| \(\mathcal{O}(f(n))\) |
big-O notation |
\mathcal{O}(f(n)) |
| \(\Omega(f(n))\) |
big-Omega notation |
\Omega(f(n)) |
| \(\Theta(f(n))\) |
big-Theta notation |
\Theta(f(n)) |
| \(p_X \left({x}\right)\) |
probability mass function (pmf) |
p_X(x) |
| \(\Pr[X=x]\) |
probability measure |
\Pr[X=x] |
| \(\operatorname{E}[X]\); \(\mu\) |
expectation |
\operatorname{E}[X] |
| \(\operatorname{Cov}(X,Y)\) |
covariance |
\operatorname{Cov}(X,Y) |
| \(\operatorname{Var}(X)\) |
variance |
\operatorname{Var}(X) |
| \(\sigma\) |
standard deviation |
\sigma |
| \(s\) |
(unbiased) sample standard deviation |
|
| \(\bar{X}\) |
sample mean |
\bar{X} |
| \(X \sim \operatorname{Pois}(\lambda)\) |
random variable that satisfies a probability distribution |
\sim |