Notation¶

Functions¶

Symbol	Meaning
$\mathbb{R}$	The set of real numbers
$\mathbb{R}^{n}$	The set of vectors of real numbers of length $n$
$\mathbb{R}^{m \times n}$	The set of matrices of real numbers of size $m \times n$

Symbol	Meaning
$f'$	Derivative of f, shorthand for $\frac{df(x)}{dx}$
$f''$	Second derivative of f
$\frac{dy}{dx}$	Derivative of y with respect to x
$\frac{d^2y}{dx^2}$	Second derivative of y with respect to x
$\frac{\partial y}{\partial x}$	Partial derivative of y with respect to x
$\frac{\partial^2 y}{\partial x^2}$	Second partial derivative of y with respect to x

Symbol	Meaning
$D_{KL}(P\|\|Q)$	KL-divergence between two distributions, P and Q

Symbol	Meaning
$x$	A vector
$X$	A matrix
$X^T$	Transpose of X
$X^*$	Conjugate transpose of X
$X^{-1}$	Inverse of X
$\|\|x\|\|_2$	Euclidean norm of x
$I$	Identity matrix
$X*Y$	Element-wise product of X and Y
$X \otimes Y$	Kronecker product of X and Y
$x \cdot y$	Dot product of x and y
$tr(X)$	Trace of X
$det(X)$	Determinant of X

Symbol	Meaning
$X$	A random variable
$P(X)$	Probability of a particular value of X. Shorthand for $P(X=x_i)$
$U(a,b)$	Uniform distribution
$N(\mu,\sigma^2)$	Normal distribution