Normalized form and resonances of matrix-valued functions of two variables

Matrix-functions that arise when solving systems of differential equations with Delta-shaped coefficients are investigated. The process of reducing the matrix-function $F(\mu,\varepsilon)$ is considered depending on two variables to the normal form by means of the matrix functions G and T such that their elements belong to a ring wide then the ring containing elements of $F(\mu,\varepsilon)$. The explicit form of the main term of expansion $[F(\mu,\varepsilon)]^{-1}$ in the case of matrices of dimension $2$ is found explicitly. The cases of resonance for systems with delta-coefficients are revealed.