I'm learning multivariate analysis. I am asked to calculate covariance of $X=\begin{pmatrix} 3&7 \\ 2&4 \\ 4&7 \end{pmatrix}$
According to P8 of Applied Multivariate Statistical Analysis written by Richard A. Johnson,
$s_{ik}=\frac{1}{n}\sum^{n}_{j=1}(s_{ji}-\bar{x}_i)(s_{jk}-\bar{x}_k)$ $i=1,2,\ldots,p$ , $k=1,2,\ldots,p$.
However, when I using R to compute covariance. It is following this formula $s_{ik}=\frac{1}{n-1}\sum^{n}_{j=1}(s_{ji}-\bar{x}_i)(s_{jk}-\bar{x}_k) $
I do not know why they are difference? How to determine when to use $\frac{1}{n}$ or $\frac{1}{n-1}$ ?