|
864
Ïĸ ¨
2011 ¹ ÖШ © ¨ ÔÔ
Û · ¢Ó · £¢Ó¿¥ ¦¦ Û Ü ¡
Îͬ£µ Õ
Ò ´¬£ Õ§, ØÕ§, ´ÊË ÕÃÝ , Õ§, ¯§ °Ë
» 2 «
1. (20 ±) x0 ÑÕ P u(x) = f(x)g′
(x) − f′
(x)g(x)
k ³·, v(x) = f(x0)g(x) − f(x)g(x0) ß°È . Ó : x0 ßÕ
P v(x) k + 1 ³·. .
2. (20 ±) A, B ÑÕ P n , X = (x1, x2, · · · , xn)′
. Æ
¥ ƶ AX = 0 ¾ BX = 0 ±© l, m ¶ ¥ ¼ ¢Ç, Å
l ≥ 0, m ≥ 0. Ì£
(1) ƶ (AB)X = 0 max{l, m} ¶ ¥ ¼ ¢Ç;
(2)
l + m > n, (A + B)X = 0 ¦ °È;
(3) ½ AX = 0 ¾ BX = 0 º» °È¢Ç, l + m = n, P n
² ¢Ç α ÀÞ ¨ α = β + γ, Å β, γ ±©Ñ AX = 0 ¾
BX = 0 ¢Ç.
3. (15 ±) A, B, C, D ß n .
A B
C D
±Ñ n, Ì£
|A| |B|
|C| |D|
= 0.
,
A ÑÀ , D = CA−1
B.
4. (15 ±) A Ñ n ¥Á V ¶ ¥§ , W Ñ V µÁ ,
AW ¨ W ²¢Ç ¡¶ µÁ , Ì:
dim(AW ) ≥ r(A) + dimW − n.
1 «
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