Geodesic
On integration of a matrix Riccati equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 101-113

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We expose the complete integration of the simplest matrix Riccati equation in the two- and three-dimensional cases for an arbitrary linear differential operator. The solution is constructed in terms of the Jordan form of an unknown matrix and the corresponding similarity matrix. We show that a similarity matrix is always representable as the product of two matrices one of which is an invariant of the differential operator.
Mots-clés : matrix Riccati equation, algebraic invariant, Jordan form. . 
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     author = {M. V. Neshchadim and A. P. Chupakhin},
     title = {On integration of a matrix {Riccati} equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {101--113},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a7/}
}
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M. V. Neshchadim; A. P. Chupakhin. On integration of a matrix Riccati equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 101-113. http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a7/