A matrix extension of the Cauchy-Schwarz inequality

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Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, background): “Here, because of the independence of the trajectoreis, we have t ; θ r t ) } T,Nt =0 ,i =0 , { p t ( s t ; θ s t ) } By Cauchy-Schwarz inequality (Tripathi, 1999), we have Then, Eq.”
Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes (2019, background): “The Matrix Cauchy-Schwarz Inequality (Tripathi, 1999) immediately shows that this is upper bounded by EﬀBd( 1 ), as is also implied by M 1 q ⊂ M 1 albeit less directly.”
ESTIMATION AND INFERENCE WITH WEAK, SEMI-STRONG, AND STRONG IDENTIFICATION (2010, unknown): “In other examples, Assumption C7 can be verified using the Cauchy– Schwarz inequality or a matrix version of it (see Tripathi (1999)) whenK(π;γ0) and H(π;γ0) take proper forms.”
On the estimation of treatment effects with endogenous misreporting (2016, unknown): “□ Since the denominator in (9), C , is always positive by the Cauchy–Schwarz Inequality (see, e.g., Tripathi, 1999) the sign of the asymptotic bias only depends on the numerator of the expression.”
Efficiently Breaking the Curse of Horizon: Double Reinforcement Learning in Infinite-Horizon Processes (2019, methodology): “By Cauchy-Schwarz inequality (Tripathi, 1999), we have Then, Eq.”