Equivalent conditions for domination of <inline-formula><tex-math id="M1">$ \mathrm{M}(2, {\mathbb C}) $</tex-math></inline-formula>-sequences

It is well known that a $ \mathrm{SL}(2, {\mathbb C}) $-sequence is uniformly hyperbolic if and only it satisfies a uniform exponential growth condition. Similarly, a $ \mathrm{GL}(2, {\mathbb C}) $-sequence whose determinants are uniformly bounded away from zero admits a dominated splitting if and only if it satisfies a uniform exponential gap condition between its the two singular values. Motivated by [19], we establish an analogous characterization for $ \mathrm{M}(2, {\mathbb C}) $-sequences that admit a dominated splitting, in terms of singular value estimates. In addition, we prove a version of the Avalanche Principle adapted to such (possibly non-invertible) complex matrix sequences.