[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"word-kvaternio":3},{"word":4,"glossSources":12,"senses":14,"sensesFi":19,"frequency":28,"etymologies":35,"etymologyFi":9,"etymologyFiLinks":9,"synonymsByPos":38,"extendedSynonymsByPos":50,"antonyms":56,"hypernyms":57,"hyponyms":63,"englishTranslations":64,"wordnetGlosses":67,"fiSynonyms":68,"fiExtendedSynonyms":69,"fiAntonyms":70,"fiExtendedAntonyms":71,"fiBaseWords":72,"fiBaseWordsGuessed":11,"fiDerivedFrom":73,"fiCompounds":74,"fiDerived":75,"fiRelated":76,"fiTranslations":77,"exampleSentences":88,"inflectionForms":101,"allInflectionForms":9,"rhymePattern":125,"rhymeSamples":126},{"id":5,"lemma":6,"pos":7,"kotusClass":8,"kotusGradation":9,"homonymIndex":9,"ipa":10,"isStub":11},161145,"kvaternio","noun",3,null,"/ˈkʋɑternio/",false,{"enWiktionary":13,"fiWiktionary":13,"wordnet":11,"aiGeneratedEn":11,"finnWordNet":13,"psychling":13,"termipankki":11},true,[15],{"index":16,"parentIndex":9,"gloss":17,"glossLinks":9,"tags":18},0,"quaternion",[],[20],{"index":16,"parentIndex":9,"glossFi":21,"glossFiLinks":22,"examplesFi":9,"tags":25,"source":27},"nelikomponenttinen luku (kompleksilukujen ulkopuolella, niiden nelikomponenttinen yleistys). Kvaterniot koostuvat reaali- ja kompleksikomponentin (i) lisäksi myös komponenteista j ja k siten, että i\u003Csup>2\u003C/sup> = j\u003Csup>2\u003C/sup> = k\u003Csup>2\u003C/sup> = ijk = -1. Yksittäisten komponenttien kertolasku toimii seuraavasti (vaaka ensimmäisenä tulontekijänä; kvaternioiden kertolasku ei ole vaihdannainen):",[23],{"text":24,"target":24},"kompleksiluku",[26],"matematiikka","fiwiktionary",{"totalAbs":29,"totalRelative":30,"avgRelative":31,"corpora":32},13,0.0049530584,0.029985484,{"s24":16,"klk":16,"lehdet":33,"wiki":34,"reddit":16,"opensub":16},0.03634378,0.14356913,[36],{"pos":9,"text":37,"links":9},"Learned borrowing from Late Latin quaterniō; sense from English quaternion.",[39],{"pos":40,"words":41},"n",[42,43,44,45,46,47,48,49],"neljä","kvartetti","nelikko","neljän ryhmä","neloset","IV","neli-","4",[51],{"pos":40,"words":52},[53,54,55],"nelikkö","nelonen","neljän pisteen nappula",[],[58,61],{"word":59,"gloss":60},"luku","one of the elements that collectively form a system of numeration; \"0 and 1 are digits\"",{"word":62,"gloss":60},"numero",[],[65],{"word":17,"type":66},"synonym",[],[],[],[],[],[],[],[],[],[],{"en":78,"pl":80,"sv":84},[79],{"word":17},[81],{"word":82,"gender":83},"kwaternion","m",[85],{"word":86,"gender":87},"kvaternion","yl",[89,95],{"paragraph":90,"matchedForm":91,"matchOffset":92,"bookId":93,"bookTitle":94,"bookAuthor":9,"bookSlug":9},"Kompleksilukujen  tavoin  myös  kvaternioille  voidaan  määritellä  yhteen -  ja  kertolasku,  mutta  toisin  kuin  reaali -  ja  kompleksiluvuilla,  niiden  kertolasku  ei  ole  kommutatiivinen.","kvaternioille",32,"https://fi.wikipedia.org/wiki/Rotaatio%20%28geometria%29","Rotaatio (geometria)",{"paragraph":96,"matchedForm":97,"matchOffset":98,"bookId":99,"bookTitle":100,"bookAuthor":9,"bookSlug":9},"Aina  näin  ei  kuitenkaan  ole,  esimerkiksi  jos  kerroinrenkaana  on  kvaternioiden  muodostama  rengas.","kvaternioiden",73,"https://fi.wikipedia.org/wiki/Ominaisarvo%2C%20ominaisvektori%20ja%20ominaisavaruus","Ominaisarvo, ominaisvektori ja ominaisavaruus",{"type":102,"essive_pl":103,"essive_sg":104,"elative_pl":105,"elative_sg":106,"abessive_pl":107,"abessive_sg":108,"ablative_pl":109,"ablative_sg":110,"adessive_pl":111,"adessive_sg":112,"allative_pl":91,"allative_sg":113,"genitive_pl":97,"genitive_sg":86,"illative_pl":114,"illative_sg":115,"inessive_pl":116,"inessive_sg":117,"partitive_pl":118,"partitive_sg":119,"accusative_pl":120,"accusative_sg":86,"comitative_pl":121,"nominative_pl":120,"nominative_sg":6,"instructive_pl":122,"translative_pl":123,"translative_sg":124},"nominal","kvaternioina","kvaterniona","kvaternioista","kvaterniosta","kvaternioitta","kvaterniotta","kvaternioilta","kvaterniolta","kvaternioilla","kvaterniolla","kvaterniolle","kvaternioihin","kvaternioon","kvaternioissa","kvaterniossa","kvaternioita","kvaterniota","kvaterniot","kvaternioineen","kvaternioin","kvaternioiksi","kvaternioksi","-io",[127,128,129],"reaktio","argumentaatio","redaktio"]