a0a2a1a4a3a6a5a2a7a2a8a2a5a10a9a12a11a10a13a14a3a15a5a14a16a15a17a10a7 2006 a18a2a19a6a20a22a21a2a23a2a24a6a25 a5a14a26a10a16a15a17a10a27a14a28a15a5a10a13a10a29a14a30a10a31a10a31a10a32 a3 a33a35a34a2a36a6a37a14a38a2a39a22a40a15a8 a41a42a40a10a43a15a37 839 a44 a45a47a46a49a48a51a50a51a52 1. a53a51a54a51a55a51a56a51a57a51a58 150 a57a51a59a61a60a51a62 a45 a54a47a63a51a64a51a65a49a66 180 a57a51a67a51a68 2 a69a61a70a51a71a51a72a51a73a51a74 a48a51a75a51a76 a72a51a77a47a78a49a79a51a59 a75a51a76 a54a51a55a51a79a51a80a51a81a51a82a47a78a49a79a47a83a49a84a51a85a51a86a51a68 1. (16 a87 ) a88a61a89 , , a90a92a91a92a93a92a94a51a95 A = 0 BB BB B@ ... ... ... 1 CC CC CA2 R n n a96a98a97a92a99a101a100a92a96a98a102a92a103 2. (16 a87 ) a104a106a105a108a107a108a109a35a110 8 >>> < >>> : a11x1 + a12x2 + + a1nxn = 0 a21x1 + a22x2 + + a2nxn = 0 an 1;1x1 + an 1;2x2 + + an 1;nxn = 0 a96a108a111 a93a108a112a35a113a106a90 A = 0 BB BB @ a11 a12 a1n a21 a22 a2n an 1;1 an 1;2 an 1;n 1 CC CC A : a114 M j(j = 1; 2; ; n) a115a108a116a108a112a35a113 A a117a119a118a35a120a106a121 j a99a108a122a108a123a108a124a35a96 n 1 a125a106a126 a100a106a103a128a127a108a129a108a130 (i) (M1; M2; ; ( 1)n 1Mn) a115a108a107a108a109a35a110 a96a108a131a106a132a108a133a108a134 (ii) a135a137a136 A a96a139a138 a90 n 1, a140a142a141a139a107a137a109a142a110 a96a139a133a137a143 a115 (M1; M2; ; ( 1)n 1Mn) a96a139a144 a93 a103 3. (16 a87 ) a145 a90 a131 a91a108a93a108a94 a127a108a146a108a147 lim n!+1 1 n n 1 !n : 4. (18 a87 ) a114 a a90a92a91a92a93a92a94 A = 0 BB BB B@ a 1 a ... ... 1 a 1 CC CC CA2 R 100 100, a95 A50 a121 a131a98a97a92a148a101a149a98a150a92a151a108a103 1 1a152a98a153a155a154a157a156a157a158a160a159a157a161a157a162a157a163 a164 1 a165 a166 2 a165 5. (18 a87 ) a145a168a167a61a169a101a110 1; 2; ; s(s > 2) a104a98a105a92a170a101a171a98a94a42a172a92a173 1 + 2; 2 + 3; ; s 1 + s; s + 1 a104a106a105a108a174a35a171a106a105 a103 6. (18 a87 ) a88a119a89a35a175a106a176a4a177a106a178a106a107a137a109 x2 + ay2 + z2 + 2bxy + 2xz + 2yz = 4 a179a35a180a119a181a108a182a108a183a35a184a139a1850 B@ x y z 1 CA = P 0 B@ x0 y0 z0 1 CA a186 a90a108a187a35a188a106a189a35a178a106a107a108a109 y02 + 4z02 = 4. a95 a; b a96a106a102a108a151 a182a108a183a108a112a35a113 P. 7. (16 a87 ) a114a108a190 a91a35a175a106a176a108a191 f(x) = x>Ax, a192a4a117 x> a115 x a96a106a193a108a194 a94 A a115 3 3 a91a108a195a108a196a108a112 a113a106a197a108a198a108a199a4a180a106a200a106a107a108a109 a130 A3 6A2 + 11A 6I = 0: a127a108a146a108a147 max A max kxk=1 f(x): a192a4a117 kxk2 = x21 + x22 + x23, a121 a131a106a132a108a201a108a202a108a102 a115a108a195a108a198a108a199a203a180a119a204a137a107a137a109 a96a139a122 a190 a91a137a195a108a196a137a112a142a113 A a205 a95 a103 8. (16 a87 )A 2 R2006 2006 a115a207a206a207a208 a96a210a209a207a211 a113 (a212 a130a214a213 a116a207a182a207a215a92a93 pa216 a123 Ap = 0 a217 Ap 1 6= 0), a127 a87a108a218a35a104a106a105a108a107a108a109a35a110 Ax = 0 (x 2 R2006) a219 a211a108a220a108a221a108a133a108a132 a93 a96a108a222a106a202a137a102a137a151a35a222a139a223a108a102a137a103 9. (16 a87 ) a114 f a115 a190a101a224a98a225 a167a61a169a35a226a108a227 V a204 a96 a104a98a105a101a184a98a185a108a94a119a228 fn a115 V a204 a96a98a229a92a230 a184a98a185a108a94a119a231a142a232 n a115a108a233 a132 a182a108a215a108a93 a103 a114 W = fv 2 V jf(v) = vg. a129a35a234 W a115 V a96a108a131a106a132 a126a35a226a108a227a106a94a106a197a108a228a108a192 a225 a93 a230a108a235 a104a106a105a35a184a106a185 (f + f2 + + fn)=n a96a106a236a108a103 2 2a152a98a153a155a154a157a156a157a158a160a159a157a161a157a162a157a163 a164 2 a165 a166 2 a165