Data matrix ($X=(x_{ij})\in {\mathbb{R}}^{n\times p}$)

A matrix representing observations and their measured variables. A common convention uses observations as rows and variables as columns; stating this orientation avoids transposition ambiguities. Column centering subtracts each variable's sample mean, and $X_c^T{X}_c/(n-1)$ is the sample covariance matrix of centered data when $n>1$.