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SUMMARY:Aleks Kleyn
DTSTART:20200601T120000Z
DTEND:20200601T140000Z
DTSTAMP:20260423T024752Z
UID:GDEq/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/6/">Sys
 tem of differential equations over quaternion algebra</a>\nby Aleks Kleyn 
 as part of Geometry of differential equations seminar\n\n\nAbstract\nThe t
 alk is based on the file\nhttps://gdeq.org/files/Aleks_Kleyn-2020.06.01.En
 glish.pdf (Russian transl.: https://gdeq.org/files/Aleks_Kleyn-2020.06.01.
 Russian.pdf)\n\nIn order to study homogeneous system of linear differentia
 l equations\, I considered vector space over division D-algebra and the th
 eory of eigenvalues in non commutative division D-algebra. I started from 
 section 1 dedicated to product of matrices. Since product in algebra is no
 n-commutative\, I considered two forms of product of matrices and two form
 s of eigenvalues (section 4). In sections 5\, 6\, 7\, I considered solving
  of homogeneous system of differential equations. In the section 8\, I con
 sidered the system of differential equations which has infinitely many fun
 damental solutions. Following sections are dedicated to analysis of soluti
 ons of system of differential equations. In particular\, if a system of di
 fferential equations has infinitely many fundamental solutions\, then each
  solution is envelope of a family of solutions of considered system of dif
 ferential equations.\n
LOCATION:https://researchseminars.org/talk/GDEq/6/
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