<prompt> Bheka isigaba esingezansi bese uphendula umbuzo emva kwalokho ngolimi olufanayo nesigaba: Ukudlula: Amaqembu e-matrix aqukethe ama-matrix kanye nokuphindaphinda kwe-matrix. Iqembu lomugqa jikelele i-GL n, R liqukethe wonke ama-matrix e-n-by-n angaguquguquki anezinto zangempela. Amaqembu ayo abizwa ngokuthi amaqembu e-matrix noma amaqembu aqondile. Isibonelo seqembu le-dihedral okukhulunywe ngaso ngenhla singabhekwa njengeqembu le-matrix elincane kakhulu. Elinye iqembu le-matrix elibalulekile yiqembu elikhethekile le-orthogonal SO n. Ichaza zonke izindlela zokuguquguquka kwezinto ezinobukhulu obungu-n. Ngama-angle ka-Euler, ama-matrix okujikeleza asetshenziswa kumidwebo yekhompyutha. Ihlolisisa iqembu ngezenzo zalo zeqembu kwezinye izindawo. Isigaba esibanzi sokumelwa kweqembu kungumfanekiso oqondile, okungukuthi, iqembu lisebenza esikhaleni se-vector, njengendawo ye-Euclidean enezinhlangothi ezintathu R3. Ukumelwa kukaG esikhaleni se-n-dimensional real vector kumane nje kuyi-homomorphism yeqembu Umbuzo: Luhlobo luni lwesikhala iqembu elisebenza kuso?  <response>: isikhala se-vector 