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 linear boundary-value problem for Noetherian linear matrix differential equation. We propose an operator, which leads linear matrix algebraic equation to the traditional linear algebraic system with a rectangular matrix. We use pseudoinverse Moore-Penrose matrices and orthogonal projections for solving linear algebraic system.