Geodesic
Bernoulli matrix equations.~II.
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 3-10

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In this paper, we find sufficient conditions for the solvability by quadratures of J. Bernoulli's equation defined over the set $M_2$ of square matrices of order 2. We consider the cases when such equations are stated in terms of bases of a two-dimensional abelian algebra and a three-dimensional solvable Lie algebra over $M_2$. We adduce an example of the third degree J. Bernoulli's equation over a commutative algebra.
Keywords: differential equation, Lie algebra.
Mots-clés : matrix equation 
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     author = {V. P. Derevenskii},
     title = {Bernoulli matrix {equations.~II.}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--10},
     publisher = {mathdoc},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_7_a0/}
}
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V. P. Derevenskii. Bernoulli matrix equations.~II.. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 3-10. http://geodesic.mathdoc.fr/item/IVM_2008_7_a0/