  We present a non-asymptotic concentration inequality for the random matrix
product \begin{equation}\label{eq:Zn} Z_n = \left(I_d-\alpha
X_n\right)\left(I_d-\alpha X_{n-1}\right)\cdots \left(I_d-\alpha X_1\right),
\end{equation} where $\left\{X_k \right\}_{k=1}^{+\infty}$ is a sequence of
bounded independent random positive semidefinite matrices with common
expectation $\mathbb{E}\left[X_k\right]=\Sigma$. Under these assumptions, we
show that, for small enough positive $\alpha$, $Z_n$ satisfies the
concentration inequality \begin{equation}\label{eq:CTbound}
\mathbb{P}\left(\left\Vert Z_n-\mathbb{E}\left[Z_n\right]\right\Vert \geq
t\right) \leq 2d^2\cdot\exp\left(\frac{-t^2}{\alpha \sigma^2} \right) \quad
\text{for all } t\geq 0, \end{equation} where $\sigma^2$ denotes a variance
parameter.
