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

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Abstract

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.

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Authors and Affiliations

  1. Donbass State Pedagogical University, ul. Generala Batyuka 19, Slavyansk, Donetsk Oblast, 84116, Ukraine

    S. M. Chuiko

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  1. S. M. Chuiko
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Correspondence to S. M. Chuiko.

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Original Russian Text © S.M. Chuiko, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 8, pp. 74–83.

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Chuiko, S.M. Generalized green operator of Noetherian boundary-value problem for matrix differential equation. Russ Math. 60, 64–73 (2016). https://doi.org/10.3103/S1066369X16080089

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