Seminar talk, 1 June 2020: Difference between revisions
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| speaker = Aleks Kleyn | | speaker = Aleks Kleyn | ||
| title = System of differential equations over quaternion algebra | | title = System of differential equations over quaternion algebra | ||
| abstract = The talk is based on the file [[Media:Aleks_Kleyn-2020.06.01.English.pdf|Aleks_Kleyn-2020.06.01.English.pdf]] | | abstract = The talk is based on the file [[Media:Aleks_Kleyn-2020.06.01.English.pdf|Aleks_Kleyn-2020.06.01.English.pdf]] (Russian transl.: [[Media:Aleks_Kleyn-2020.06.01.Russian.pdf|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. | 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. | ||
| video = | |||
Language: English | |||
<code>Zoom Meeting at https://us02web.zoom.us/j/88481953966 | |||
Meeting ID: 884 8195 3966</code> | |||
| video = https://video.gdeq.org/GDEq-zoom-seminar-20200601-Aleks_Kleyn.mp4 | |||
| slides = | | slides = | ||
| references = | | references = | ||
| 79YY-MM-DD = 7979-93-98 | | 79YY-MM-DD = 7979-93-98 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
Speaker: Aleks Kleyn
Title: System of differential equations over quaternion algebra
Abstract:
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.
Language: English
Zoom Meeting at https://us02web.zoom.us/j/88481953966
Meeting ID: 884 8195 3966
Video