title: Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.
abstract: Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.
authors.affiliation: Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601, Ukraine.
authors.forename: Vyacheslav M
authors.initials: VM
authors.lastname: Boyko
authors.forename: Roman O
authors.initials: RO
authors.lastname: Popovych
authors.forename: Nataliya M
authors.initials: NM
authors.lastname: Shapoval
keywords: Lie symmetry; Matrix equation; System of second-order ordinary differential equation