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This paper studies the deviation inequality for the spectral norm of randommatrices with dependent entries. In particular, we consider a random matrix$BA$, where $A$ is a random matrix with independent mean zero subexponentialentries, and $B$ is a deterministic matrix. We obtain an exponential inequalityfor the spectral norm of an $m\times n$ matrix $BA$ using a comparison theoremdue to Latala, van Handel and Youssef. Applying this result, we prove anestimate of the smallest singular value of a random subexponential matrix.

Deviation Inequalities on the Spectral Norm of Random Matrices with Dependent Entries