 Solution

Using divisor $n=4$, the covariance matrix isFor example, the first variance is $(1+1+1+9)/4=3$, and the first-second covariance is $(3-1-1+3)/4=1$. If “sample covariance matrix” means the unbiased convention, use divisor $n-1=3$ instead: $S=(4/3)\Sigma$. This multiplies every eigenvalue by $4/3$ and leaves all principal component loadings and explained-variance fractions unchanged.