A datapoint, instance, sample, or observation, is a unit of data in a dataset. When datasets are tabular, $x_{ij}$ usually represents the value of the $j$th variable (attribute) in the $i$th data point, where $i=1,2,...,n$ indicates the index of the data point and $j=1,2,...,p$ identifies the variable. This way, a dataset can be represented as an $n\times p$ matrix $X$, where the row (or vector) $x_i$ represents a datapoint that consists of the $p$ values of $x_{i1}, x_{i2}, x_{i3}, \dots , x_{ip}$ corresponding to each variable. $X=\begin{bmatrix} x_{11} & x_{12} & x_{13} & \dots & x_{1p} x_{21} & x_{22} & x_{23} & \dots & x_{2p} \vdots & \vdots & \vdots & \ddots & \vdots x_{n1} & x_{n2} & x_{n3} & \dots & x_{np} \end{bmatrix} =\begin{bmatrix} x_1^T x_2^T \vdots x_n^T \end{bmatrix}$