Geodesic
Generalized Green operator of Noetherian boundary-value problem for matrix differential equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 74-83

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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.
Keywords: Green operator, Noetherian boundary value problem, matrix differential equation. 
@article{IVM_2016_8_a7,
     author = {S. M. Chuiko},
     title = {Generalized {Green} operator of {Noetherian} boundary-value problem for matrix differential equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--83},
     publisher = {mathdoc},
     number = {8},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_8_a7/}
}
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S. M. Chuiko. Generalized Green operator of Noetherian boundary-value problem for matrix differential equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 74-83. http://geodesic.mathdoc.fr/item/IVM_2016_8_a7/