Seminar talk, 1 June 2020
Speaker: Aleks Kleyn
Title: System of differential equations over quaternion algebra
The talk is based on the file Aleks_Kleyn-2020.06.01.English.pdf (Russian transl.: Aleks_Kleyn-2020.06.01.Russian.pdf)
In order to study homogeneous system of linear differential equations, I considered vector space over division D-algebra and the theory of eigenvalues in non commutative division D-algebra. I started from section 1 dedicated to product of matrices. Since product in algebra is non-commutative, I considered two forms of product of matrices and two forms of eigenvalues (section 4). In sections 5, 6, 7, I considered solving of homogeneous system of differential equations. In the section 8, I considered the system of differential equations which has infinitely many fundamental solutions. Following sections are dedicated to analysis of solutions of system of differential equations. In particular, if a system of differential equations has infinitely many fundamental solutions, then each solution is envelope of a family of solutions of considered system of differential equations.
Zoom Meeting at https://us02web.zoom.us/j/88481953966
Meeting ID: 884 8195 3966