Generalized green operator of Noetherian boundary-value problem for matrix differential equation

We find necessary and sufficient conditions for solvability and the construction of the generalized Green operator for Noetherian linear boundary-value problem for a linear matrix differential equation. We propose an operator, which leads a linear matrix algebraic equation to the traditional linear algebraic system with a rectangular matrix. We use pseudoinverseMoore–Penrose matrices and orthogonal projections for solving a linear algebraic system.