向量组线性相关性的几种判定方法

582008O151A1673999X200801005802...12,,,(1)ssααα≥F12,,,skkk11220sskkkααα+++=12,,,sααα12,,,sααα.1112223,,βααβαα=+=+334,βαα=+441,βαα=+1234,,,ββββ.1234,,,kkkk112233440kkkkαααα+++=112223,,βααβαα=+=+334,βαα=+441,βαα=[phone]()()()()0kkkkkkkkαααα+++++++=131kk==241kk==−112233440kkkkαααα+++=1234,,,ββββ.12,,,(2)ssααα≥αα0α=.14132ββββ=+−4β1234,,,ββββ..12,,,sααα12,,,sααα.2()()()1232,1,1,1,0,3,2,0,2,4,3,1ααα=−−=−=−.123,,ααα13123123132203402300kkkkkkkkkk+=⎧⎪++=⎪⎨−−+=⎪⎪−−=⎩2007101720083Mar.20081JournalofYiliNormalUniversityNaturalScienceEditionNo.11591323,kkkk=−=−1231,1kkk==−=123,,ααα...2123,,αααA202101134011123000101000⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥→⎢⎥⎢⎥−−⎢⎥⎢⎥−−⎣⎦⎣⎦23123,,ααα123,,ααα123,,ααα.12,,,sαααss12,,,sααα()12,,,sAααα=As10A=12,,,sααα20A≠12,,,sααα.312,,,mααα11122mmmkkkαααα+=+++0ik≠1,2,,im=.121,,,,mmαααα+m.1mα+12,,,mααα.1111,,,,,(11)iimimαααα−++≤≤+121,,,mkkk+111111110iiiimmkkkkαααα−−+++++++++=10mk+≠111111111111111111111110iimiimmiiimiiiimmmmmmmmmkkkkkkkkkkkkkkkkkkαααααααααα−+−++−++−++++++++++=+++++=++++++iα0ik≠..n+1n..SeveralKindsofMethodsforJudgingtheRelatedLinearityofVectorsGroupXIAOAi-ping(LianyungangTeacher’College,Lianyungang222006,Jiangsu)Abstract:Thejudgingmethodsofthevectorsgrouprelateddependencefromdeterminantvalues,rankofmatrix,solutionofsystemoflinearequationsetcwerestudied.Thispaperinducessixkindsofmethodsforjudgingtherelatedlinearityofvectorsgroup.Keywords:vectorsgroup;relatedLinearity;irrelevantlinearity;judgingmethods