Involyuciya involyucijna funkciya v matematici ce funkciya sho ye obernenoyu sama do sebe Involyucijna funkciya f X X displaystyle f X to X zastosovana dvichi povertaye nas v pochatkovu tochku Formalno ce biyektivne vidobrazhennya f X X displaystyle f X mapsto X sho maye vlastivist f f x x x X displaystyle f f x x quad forall x in X Zmist 1 Vlastivosti 2 Perestanovki 3 Involyuciya v Evklidovij geometriyi 4 Involyuciya v linijnij algebriVlastivosti Redaguvati x f 1 x f x displaystyle forall x qquad f 1 x f x nbsp x y f x y f y x displaystyle forall x exists y f x y f y x nbsp Perestanovki RedaguvatiPerestanovka t displaystyle tau nbsp ye involyuciyeyu yaksho t t i d displaystyle tau circ tau id nbsp Kozhna involyuciya ye dobutkom transpozicij Napriklad 1 2 3 4 5 6 7 8 5 7 4 3 1 8 2 6 1 5 2 7 3 4 6 8 displaystyle begin pmatrix 1 amp 2 amp 3 amp 4 amp 5 amp 6 amp 7 amp 8 5 amp 7 amp 4 amp 3 amp 1 amp 8 amp 2 amp 6 end pmatrix 1 5 2 7 3 4 6 8 nbsp Involyuciya v Evklidovij geometriyi RedaguvatiInvolyuciyami ye vsi simetriyi centralna osova a takozh inversiya vidnosno kola Involyuciya v linijnij algebri RedaguvatiV linijnij algebri involyuciya ce linijnij operator T displaystyle T nbsp sho maye vlastivist T 2 I displaystyle T 2 I nbsp Involyuciya pov yazana z idempotentnimi operaciyami Yaksho a displaystyle a nbsp idempotent to 1 2 a displaystyle pm 1 2a nbsp ye involyuciyami Yaksho b displaystyle b nbsp involyuciya todi 1 b 2 displaystyle frac 1 b 2 nbsp ta 1 b 2 displaystyle frac 1 b 2 nbsp ye ortogonalnimi idempotentami nbsp Ce nezavershena stattya z matematiki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Otrimano z https uk wikipedia org w index php title Involyuciya matematika amp oldid 33963951
