  In this paper we obtain a Bernstein type inequality for the sum of
self-adjoint centered and geometrically absolutely regular random matrices with
bounded largest eigenvalue. This inequality can be viewed as an extension to
the matrix setting of the Bernstein-type inequality obtained by Merlev\`ede et
al. (2009) in the context of real-valued bounded random variables that are
geometrically absolutely regular. The proofs rely on decoupling the Laplace
transform of a sum on a Cantor-like set of random matrices.
