Ko te rōpū rārangi whānui ko te GL ((n, R) ngā katoa o te n-i runga i te-n matrix invertible ki ngā tomokanga tūturu. E kiia ana ona rōpū raro rite rōpū matrix ranei ngā rōpū rārangi. Ka taea te tirohia te tauira rōpū dihedral whakahuatia i runga ake nei rite te rōpū matrix (iti rawa). Ko tētahi atu rōpū matrix nui ko te rōpū motuhake ōrite SOn ((). E whakaahua ana te reira i nga huringa katoa e taea i roto i n ahu. Via koki Euler, e whakamahia huringa matrix i roto i te whakairo rorohiko. Te ariā whakaaturanga ko e rua te tono o te ariā rōpū, me te nui mo te māramatanga hohonu o ngā rōpū. ako reira i te rōpū e ona mahi i runga i ētahi atu mokowā. he whānui rōpū o ngā whakaaturanga he whakaaturanga rārangi noa, ara, ko te rōpū mahi i runga i te wāhi vector toru-ahu, pērā i te wāhi Euclidean.
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