Nehaj A a i j displaystyle A a ij kvadratna matricya poryadku n displaystyle n v yakij vibrano dovilni k displaystyle k ryadkiv z nomerami i 1 lt i 2 lt lt i k displaystyle i 1 lt i 2 lt ldots lt i k ta dovilni k displaystyle k stovpciv z nomerami j 1 lt j 2 lt lt j k displaystyle j 1 lt j 2 lt ldots lt j k Zmist 1 Viznachennya 1 1 Prikladi 2 Div takozh 3 DzherelaViznachennya RedaguvatiAlgebrayichne dopovnennya minora M j 1 j k i 1 i k displaystyle M j 1 ldots j k i 1 ldots i k nbsp viznachayetsya tak A j 1 j k i 1 i k 1 p q M j 1 j k i 1 i k displaystyle A j 1 ldots j k i 1 ldots i k 1 p q overline M j 1 ldots j k i 1 ldots i k nbsp de p i 1 i k q j 1 j k displaystyle p i 1 ldots i k quad q j 1 ldots j k nbsp M j 1 j k i 1 i k displaystyle overline M j 1 ldots j k i 1 ldots i k nbsp dopovnyuvalnij minor Algebrayichnim dopovnennyam elementa a i j displaystyle a ij nbsp nazivayut minor cogo elementa vzyatij zi znakom 1 i j displaystyle 1 i j nbsp tobto A i j 1 i j M i j displaystyle A ij 1 i j M ij nbsp Prikladi Redaguvati Minor M 23 displaystyle M 23 nbsp kvadratnoyi matrici A displaystyle A nbsp viznachnik matrici otrimanij shlyahom vikreslyuvannya ryadka 2 ta stovpchika 3 A 1 4 7 3 0 5 1 9 11 M 23 1 4 1 9 displaystyle A begin pmatrix 1 amp 4 amp 7 3 amp 0 amp 5 1 amp 9 amp 11 end pmatrix qquad M 23 begin vmatrix 1 amp 4 amp Box Box amp Box amp Box 1 amp 9 amp Box end vmatrix nbsp displaystyle longrightarrow nbsp 1 4 1 9 9 4 13 displaystyle begin vmatrix 1 amp 4 1 amp 9 end vmatrix left 9 left 4 right right 13 nbsp Znajti algebrayichni dopovnennya elementiv a21 ta a33 viznachnika 2 3 1 1 4 2 3 1 4 displaystyle begin vmatrix 2 amp 3 amp 1 1 amp 4 amp 2 3 amp 1 amp 4 end vmatrix nbsp Rozv yazok Algebrayichni dopovnennya do elementiv a21 ta a33 poznachimo A21 ta A33 vidpovidno Znahodzhennya minoriv nbsp Pidstavimo ci znachennya minoriv u vidpovidni rivnosti 4 oderzhimo shukani algebrayichni dopovnennya A21 1 2 1 M21 13 A33 1 3 3 M33 5Div takozh RedaguvatiTeoriya matric Matricya Viznachnik Teorema Laplasa Soyuzna matricyaDzherela RedaguvatiGantmaher F R Teoriya matric 5 e M Fizmatlit 2010 559 s ISBN 5 9221 0524 8 ros Otrimano z https uk wikipedia org w index php title Algebrayichne dopovnennya amp oldid 18940484
