สมบ, การสล, บท, ในคณ, ตศาสตร, งกฤษ, commutativity, อกระบวนการเปล, ยนลำด, บของบางส, โดยไม, ทำให, ผลล, พธ, ดท, ายเปล, ยนแปลง, เป, นสมบ, เบ, องต, นของการดำเน, นการทางคณ, ตศาสตร, หลายชน, และการพ, จน, หลายอย, างก, นอย, บสมบ, วอย, างแสดงของการบวก, ของการดำเน, นการพ,. inkhnitsastr smbtikarslbthi xngkvs commutativity khuxkrabwnkarepliynladbkhxngbangsing odyimthaihphllphthsudthayepliynaeplng epnsmbtiebuxngtnkhxngkardaeninkarthangkhnitsastrhlaychnid aelakarphisucnhlayxyangkkhunxyukbsmbtinitwxyangaesdngsmbtikarslbthikhxngkarbwk 3 2 2 3 smbtikarslbthikhxngkardaeninkarphunthan xathikarbwkhruxkarkhunkhxngcanwn thuksmmtikhunodyirkhxkngkhamaepnewlayawnan aelasmbtiniimekhymikartngchuxhruxkarihehtuphlcnkrathngkhriststwrrsthi 19 sungepnchwngewlathinkkhnitsastrerimcdraebiybaebbaephnkhxngthvsditang thangkhnitsastr enuxha 1 karichthwip 2 niyam 3 twxyang 3 1 kardaeninkarslbthiidinchiwitpracawn 3 2 kardaeninkarslbthiidinkhnitsastr 3 3 kardaeninkarslbthiimidinchiwitpracawn 3 4 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swnkardaeninkarthiimepniptamenguxnikhdanbn cathuxwaepnkardaeninkarthi slbthiimid hrux imslbthi non commutative eraxacklawidwa x samarth slbthi kb y phayitkardaeninkar thahak x y y x displaystyle x y y x kahndfngkchnthwiphakh f A A B eracaklawwafngkchnnn slbthiid thahak x y A f x y f y x displaystyle forall x y in A f x y f y x twxyang aekikhkardaeninkarslbthiidinchiwitpracawn aekikh karisrxngethakehmuxnkbkardaeninkarslbthiid ephraaimsakhywacaisrxngethakhangsayhruxkhangkhwakxn phlsudthaykehmuxnknkhuxidisrxngethathngsxngkhang inkaraelkepliynengintra erasamarthichpraoychncaksmbtikarslbthikhxngkarbwk sungimsakhywaeracaaelkepliynxairkxn phllphthsudthaykcarwmknidethaedimkardaeninkarslbthiidinkhnitsastr aekikh twxyangkardaeninkarthwiphakhthimismbtikarslbthi sungepnthiruckkndiidaek 3 karbwkkhxngcanwncring slbthiidenuxngcak y z z y y z R displaystyle y z z y quad forall y z in mathbb R twxyangechn 4 5 5 4 sungniphcnthngsxngkhangmikhaethakb 9 karkhunkhxngcanwncring slbthiidenuxngcak y z z y y z R displaystyle yz zy quad forall y z in mathbb R twxyangechn 3 5 5 3 sungniphcnthngsxngkhangmikhaethakb 15twxyangkardaeninkarxun echn karbwkaelakarkhunkhxngcanwnechingsxn karbwkkhxngewketxr xinetxreskchnaelayueniynkhxngest epntn kardaeninkarslbthiimidinchiwitpracawn aekikh kartxsayxkkhra concatenation imsamarthslbthiid karskphaaelakartakphakehmuxnkbkardaeninkarslbthiimid ephraathahakeratakphakxnskpha phllphthcatangipcakthieraskphakxnaelwkhxytak lukbaskkhxngrubikhimsamarthslbthiid echn thahakbidswnhnatamekhmnalika swnbntamekhm aelaswnhnathwnekhm FUF hnabnlukbaskcaihphlimehmuxnkbkarbidswnhnatamekhm aelabidthwnekhmklb tamdwyswnbntamekhm FF U ladbkarbidlukbaskkhxngrubikhcungslbthiimid epnkrnihnungthimikarsuksainthvsdikrupkardaeninkarslbthiimidinkhnitsastr aekikh twxyangkardaeninkarthwiphakhthiimmismbtikarslbthiechn 5 karlb ephraawa 0 1 1 0 karhar ephraawa 1 2 2 1 karkhunkhxngemthriks ephraawa 0 2 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 displaystyle begin bmatrix 0 amp 2 0 amp 1 end bmatrix begin bmatrix 1 amp 1 0 amp 1 end bmatrix cdot begin bmatrix 0 amp 1 0 amp 1 end bmatrix neq begin bmatrix 0 amp 1 0 amp 1 end bmatrix cdot begin bmatrix 1 amp 1 0 amp 1 end bmatrix begin bmatrix 0 amp 1 0 amp 1 end bmatrix okhrngsrangthangkhnitsastrxun aekikhxabieliynkrup khuxkrupthimikardaeninkarkhxngkrup thislbthiid 2 ringslbthi khuxringthimikarkhun thislbthiid sahrbkarbwknnslbthiidxyuaelwtamniyam 2 infildhnung thngkarbwkaelakarkhunsamarthslbthiid 2 xangxing aekikh Axler Sheldon 1997 Linear Algebra Done Right 2e Springer ISBN 0 387 98258 2 2 0 2 1 2 2 2 3 Gallian Joseph 2006 Contemporary Abstract Algebra 6e ISBN 0 618 51471 6 3 0 3 1 Krowne Aaron Commutative at PlanetMath ekhathungemux 8 singhakhm 2550 exrik dbebilyu iwssitn Commute cakaemthewild ekhathungemux 8 singhakhm 2550 Yark Examples of non commutative operations at PlanetMath ekhathungemux 8 singhakhm 2550 duephim aekikhsmbtikarslbthiklbekhruxnghmay anticommutativity smbtikarepliynhmu smbtikaraeckaecngekhathungcak https th wikipedia org w index php title smbtikarslbthi amp oldid 8363449, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,