Notation

Description	Example	Meaning
Lower case j	$\underline{x}^j$	Number of coordinate of vector $\underline{x}$
Lower case i	$\underline{x}_i = (x^1_i, \dots, x^p_i)'$	Identify one specific observation of a (column) vector of the explanatory variables
Parenthesis to apply power	$\left( x_i^j \right)^2$	Denotes the power of the $j$-th variable for the $i$-th observation
Caligraphic J	$x^\mathcal{J}$	Denotes a subset of indices
Negative Mathematical J	$x^{-\mathcal{J}}$	Removing the $j$-th coordinate
$=z$	$\underline{x}^{j|=z}=(x^1, \dots, x^{j-1}, z, x^{j+1}, \dots, x^p)'$	Replaces the $j$-th component of vector $\underline{x}$ with $z$