  We present a new finite-time analysis of the estimation error of the Ordinary
Least Squares (OLS) estimator for stable linear time-invariant systems. We
characterize the number of observed samples (the length of the observed
trajectory) sufficient for the OLS estimator to be $(\varepsilon,\delta)$-PAC,
i.e., to yield an estimation error less than $\varepsilon$ with probability at
least $1-\delta$. We show that this number matches existing sample complexity
lower bounds [1,2] up to universal multiplicative factors (independent of
($\varepsilon,\delta)$ and of the system). This paper hence establishes the
optimality of the OLS estimator for stable systems, a result conjectured in
[1]. Our analysis of the performance of the OLS estimator is simpler, sharper,
and easier to interpret than existing analyses. It relies on new concentration
results for the covariates matrix.
