[理學(xué)]線性代數(shù)ii-chapter-展示頁(yè)
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【正文】 T h eRemarks ? ?c ol u m n s . ofn u m be r t h e t oe qu a l ism a t r i x s qu a r e ai n r ow s ofn u m be r t h es,ot h e r w or dI n .)( de n ot e d a n dor de r ofm a t r i x s qu a r e a c a l l e d ism a t r i x A n 1nnijaAnnn???? ?? ?. ofs u bm a t r i x t h ec a l l e d is c o l u m n s a n d r o w s i t s of a l ln o t c o u r s e ofb u t s o m e d e l e t i n gb y m a t r i x g i v e n a f r o m o b t a i n e dm a t r i x A 2AA(3) The term matrix was first introduced by British mathematician James Joseph Sylvester in 1890. ? ?? ? v e c t o r .r o w a c a l l e d is t h e n ,1 if ,m a t r i x aF o r 4112111 nnnmaaaAmA?????t o r .c o l u m n v e c a c a l l e d is t h e n ,1 If1111???????????? ?mmaaAn ?? ?m a t r i x . 11 t h easu p o n l o o k e d bem a y n u m b e r a is t h a t s c a l a r , a is t h e n ,1 If11111111????? ?aaaAmnThe followings are some kinds of special matrices: ? ? 。,...,(di a g00Λ: t h i sl i ke l ook sI t m a t r i x . di a g on a l a c a l l e d is t h e n z e r o is di a g on a l on t h en ot is t h a t ofe n t r y e a c h If2121nnAA?????????????????????( c ) A n m a tr ix is c a l l e d a n ide ntit y m a tr ix if it is a d ia go na l m a tr ix a nd a l l a l l the e nt r ie s o n the dia go na l a r e e qu a l to 1. I t l oo ks l ike t his:1 1nnE????????????The diagonal matrices form an important class of matrices in the matrix theory. Matrices that can be transformed to diagonal matrices by premultiplying and postmultiplying with suitable matrices are of special importance. m a t i x a n y is w h e r e ism a t r i x i de n t i t y t h eofpr ope r t y i m por t a n t A n nnAAEAAEnn????( d) A n m a tr ix i s c a l l e d a n upp e r ( l ow er) tr ia ngu l a r m a tr ix i f a l l e ntr ie s be l ow ( a bov e ) t he dia gon a l a r e z e r o. I t l ook s l ike t his :n n A?。...0...0...0m a t r i x n g u l a r l o w e r t r i aA 21222111?????????????nnnnaaaaaaA????? ?? ? m a t r i x s y m m e t r i c a c a l l e d is m a t r i x s q u a r e t h e n t h e,2,1, , e n t r i e s t h eIf fnn ?? ???ijnnjiijaAnjiaa ?Like diagonal matrices, triangular matrices form an important class of matrices in the matrix theory. ,0000000 f or me c h e l on R o w ( h )2222111211?????????????????????????????????????????rnrrnrnraaaaaaaaaA? ?? ? nng I f th e e n tr ie s , , 1 , 2 , , , th e n th e s q u a r e m a tr ix is c a l l e d a s k e w s y m m e tr ic m a tr ixi j j in n i ja a i j nAa ??? ? ??r o w . p r e v i o u s t h eofe n t r y n o n z e r of i r s t t h e ofr i g h t t h e t ois r o wa n y i n e n t r y n o n z e r of i r
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