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We prove the following operator-coefficients free Poincar\'{e} inequality:$$|f(X)-E[f(X)]|_{2}\leq2|X|_{2}\|\widehat{\partial}_{X:B}[f(X)]\|_{\pi}, \quadf(X) \in \mathrm{dom}(\widehat{\partial}_{X:B}),$$ where $\|\cdot\|_{\pi}$ isthe projective tensor norm.

An operator-coefficients free Poincar\'e inequality