Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories

The paper proves a nonasymptotic high-probability bound on the least-squares estimator Ĝ via the innovations-form regression, controlling (Y−Y−*)−1, a Gaussian cross term, and mean-dependent terms; see the exact identity, estimator, decomposition, and Theorem 1 with the same ε1, ε2, ε3 and thresholds N0, N1, N2 in the paper . The candidate solution reproduces this argument step-by-step (same regression identity, the same Gram lower bound, the same scaling for S1 via Gaussian concentration, and the same linear/quadratic-in-‖X̂0‖ terms), differing only in technique for the cross term S1 (matrix Bernstein vs the paper’s Gaussian product lemma) but yielding the same bound and constants.