VI ma Han A=(a n) khong suy men, nen co ma tran nghich dge 11 = A ' = (bd.
5.Dinh lY chi se quail tinh va dinh Hi Sylvester Gia su fi la mot don ft 'man phvong teen 14 khOng gian vec to V.
H &toe goi la xac dinh n6u Mix) * 0 v6i moi x s O.
H dti0c goi la xac dioh doting nen I4(x) > 0 \FM moi x x 0. H dvoc goi IA xac dinh Am n6u 14(x) < 0 veli moi x* 0.
Dinh 19
Cho V la R. - khong gian vec to n chi6u. H la dung town hiving tren V thi V la tong true 061) true giao (doi v6i H) clia a khong gian Vo, V,, Vs
V = V. CS V. ff) Vo ma HIV, la xac (huh during, HIV_ la xac inh am, H I V0 = 0. Cach phan tich tren khong duy nhal nhvng o luon ]a hod) cem H, dim V. = p, dim V. = q khong (16i; p, q leo OM to goi la chi s6 dtiong van 'al-1h, chi s6 am (man tinh Oa H (hay ens clang eve 0 cim no).
Dinh ly Sylvester
Gia sit V la R - khong gian vec to n chigu. H la clang to pfuldng tren V, A la ma tran cua clang Loan phudng H tro mat cd sa nao do Goi Ak la ma trail con ;oiling cap k a goc tr ben trai cim ma trail A (Ak tao bai giao cua k clang <tau va k ( dau elm ma trail A). Khi do:
H Ea clang toan pinicing xac dinh dining khi va chi k det Ak > 0 vdi rani k = 1, 2, n.
H le dang toan phuong xac dinh am khi va chi khi det Ak %
vdi k than va det Ak < 0 vdi k Le.
Chu 9: Khi H có ma tran dti). 'clang A, n6u H )(lc dinh duct to cling noi ma trail A 'the dinh ducing.
§ 2 KH6NG WAN VEC TO OCLIT
1. Dinh nghia
Cho E la khong gian vec to tren truiing s6 tlnic R. Ta mat tich ve hudng a tren E la mkt anh xa song tuy6n tinh, xilng va xac dinh dining lien E, ki hiou ban <,> hay (. , .), ngh la to co: < >; E x E R la anh xa song tuy6n tinh
thOa man (x, x) > 0 vdi moi x E 1E va <x, x> = 0 suy ra x = 0. Khong gian vec td E cling vdi mot tich va hung xac dii tren E dnpc goi la nEat khong gian vec Ed (Mit.