TY - JOUR

T1 - On Integration of a Matrix Riccati Equation

AU - Neshchadim, M. V.

AU - Chupakhin, A. P.

N1 - Funding Information: The authors were supported by the Programs of Basic Research nos. III.22.4.1 and I.1.5 (project no. 0314–2019–0011) of the Siberian Branch of the Russian Academy of Sciences. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/11

Y1 - 2020/11

N2 - We execute the complete integration of the simplest matrix Riccati equation in the two- andthree-dimensional cases for an arbitrary linear differential operator. The solution isconstructed in terms of the Jordan form of an unknown matrix and the corresponding similaritymatrix. We show that a similarity matrix is always representable as the product of two matricesone of which is an invariant of the differential operator.

AB - We execute the complete integration of the simplest matrix Riccati equation in the two- andthree-dimensional cases for an arbitrary linear differential operator. The solution isconstructed in terms of the Jordan form of an unknown matrix and the corresponding similaritymatrix. We show that a similarity matrix is always representable as the product of two matricesone of which is an invariant of the differential operator.

KW - algebraic invariant

KW - Jordan form

KW - matrix Riccati equation

UR - http://www.scopus.com/inward/record.url?scp=85100385214&partnerID=8YFLogxK

U2 - 10.1134/S1990478920040110

DO - 10.1134/S1990478920040110

M3 - Article

AN - SCOPUS:85100385214

VL - 14

SP - 732

EP - 742

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -