ממן14

ממן14 - 14 " 1...

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Unformatted text preview: 14 " 1 : U - : , 1 4 -1 3 1 - . A = 5 0 5 K 10 0 5 3 1 0 0 -5 1 0 2 B 0 = 0 1 0 0 .1 . , , A , - B . U - , - U {x 3 - 5, x 2 + 2, x} . dim U = 3 ,- , U : W - : , 1 0 -2 4 2 1 1 D 0 = 0 0 0 0 1 4 0 6 2 -m1 5 K 1 , . C = 2 -3 9 2 D . , , C - . dim W = 2 - W - {x 3 - 2 x + 4, x 2 + x + 1} : U + W - U + W = Sp({x 3 + 4 x 2 - x + 3, x 3 + 5 x 2 + 5,3 x 3 + 10 x 2 + 5, , x 3 + 4 x 2 + 6, x 3 + 2 x 2 - x + 5, 2 x 3 + 2 x 2 - 3 x + 9}) ,V.16 . : 1 4 -1 5 0 1 10 0 3 F . E = 1 4 0 2 -1 1 2 2 -3 3 5 5 K 6 5 9 1 0 0 0 0 0 0 1 0 0 0 0 0 10 0 -1 1 3 = F 0 0 0 0 0 0 , , , - . dim(U + W ) = 3 - U + W - {x 3 + 10, x 2 - 1, x + 3} . dim(U + W ) = dim U + dim W - dim(U W ) , . dim(U W ) = 2 - : U A W - ,V.29 , dim(U W ) = 2 = dim W , U W W . {x 3 - 2 x + 4, x 2 + x + 1} : , U W = W .2 2 : A = {v1 , v2 ,K , vk , a} - b , , V A b , , b A Sp(C ) . b = 1v1 + 2 v2 + K + k vk + k +1 a : k +1 - . k +1 , 0 , C = {v1 , v2 ,K , vk } - .1 1 b = 1 v1 + 2 v2 + K + k vk + a k +1 k +1 k +1 k +1 a . a = 1 b - 1 v1 - 2 v2 - K - k vk k +1 k +1 k +1 k +1 . a A Sp( B) , B = {v1 , v2 ,K , vk , b} . v = 1v1 + 2 v2 + K + k vk + k +1 a , V A . v A V .2 1 v = 1v1 + 2 v2 + K + k vk + k +1 b - 1 v1 - 2 v2 - K - k vk = k +1 k +1 k +1 k +1 = 1 - k +1 1 1 + 2 - k +1 2 2 + K + k - k +1 k k + k +1 v v v b k +1 k +1 k +1 k +1 :' B , , B V - , . V : - A - . - C - 1v1 + 2 v2 + K + k vk + k +1 a = 0 , k +1 = 0 . A , - C - , C . - A , , 1 = 2 = K = k vk = k +1 = 0 . k +1 - : k +1 . a = - 0 - .3 1 v1 - 2 v2 - K - k vk k +1 k +1 k +1 , ,' a = 1 b - 1 v1 - 2 v2 - K - k vk k +1 k +1 k +1 k +1 , 1 b - 1 v1 - 2 v2 - K - k vk = - 1 v1 - 2 v2 - K - k vk k +1 k +1 k +1 k +1 k +1 k +1 k +1 k v v v . b = 1 - k +1 1 1 + 2 - k +1 2 2 + K + k - k +1 k k +1 k +1 k +1 . b A Sp(C ) , C b . - A , k +1 = 0 , A . V , - A . V - 3 - , . U = Sp({v1 , v2 , v3 }) , U {v1 , v2 , v3 } .( U {v1 , v2 , v3 } - ) dim U A 3 ,V.27 , U B = {u1 - u2 , u1 + 3u3 , 4u2 + 5u3 } - U - , u1 , u2 , u3 A U ,V.27 , - B - . . dim U = 3 - , . dim U A 3 . dim V = dim U1 + dim U 2 ,V.32 . V = U1 U 2 - .2 .1 , , dim(U1 W ) = dim{0} = 0 , U1 W = {0} . dim(U1 + W ) = dim U1 + dim W - dim(U1 W ) = dim U1 + dim W .V.29 dim(U1 + W ) , . dim U1 + dim W dim V , , U1 ,W A V , U1 + W V dim U1 + dim U 2 : - . dim W A dim U 2 : . W U 2 {0} . W A {0} 2 . V = R , U1 = {(a, 0) | a R}, U 2 = {(0, b) | b R}, W = {(c, c ) | c R} (a, b) A R 2 , V = U1 U 2 . V - W , U1 ,U 2 . U1 U 2 = {(0, 0)} = {0} , (a, b) = (a, 0) + (0, b) , (1,1) A W W A {0} - , U1 W = {(0, 0)} = {0} . W U 2 = {(0, 0)} = {0} 4 A A2 . A2 = 0 - , ,( 1 A j n ) j A [ A] A j = 0 , . .1 , Ax = 0 A - . A . Ax = 0 P ( A) - ) , P ( A) - A , P ( A) - , ( A) , ( A) dim P( A) ,(V.29 n ( A) , . dim P ( A) = n - ( A) ,V.45 . - . ( A) n , 2 .2 P ( A) - . ( A2 ) < ( A) , , dim P ( A) = n - ( A) . P ( A2 ) , Ax = 0 .( n A n A2 ) ( A2 ) = n - dim P( A2 ) , ( A) = n - dim P( A) , . dim P ( A) < dim P ( A2 ) , , n - dim P ( A2 ) < n - dim P( A) , A2 y = 0 . y A P ( A) - y A P ( A2 ) . , Ay A 0 2 A , . ( A ) y = 0 , , A y = 0 , ( n A1 ) Ay , . A( Ay ) = 0 , - , , Ay A 0 . Ax = 0 . 5 , . W B = {v1 , v2 , v3 } - : - . B 1v1 + 2 v2 + 3 v3 = 0 , . 1 (1, 2, 2,1) + 2 (0, 2, 0,1) + 3 (-2, 0, -4,3) = 0 : . (1 , 21 , 21 , 1 ) + (0, 22 , 0, 2 ) + (-23 , 0, -43 ,33 ) = 0 . (1 - 23 , 21 + 22 , 21 - 43 , 1 + 2 + 33 ) = 0 : .1 1 - 23 = 0 21 + 22 = 0 : . 21 - 43 = 0 1 + 2 + 33 = 0 1 2 1 = 2 = 3 = 0 : . A = 2 1 0 -2 2 0 K 0 -4 1 3 1 0 0 0 0 1 0 0 0 0 A = 1 0 B . . W - - B , . . W v , v A W - 1 , 2 , 3 . B ,' . 1 (1, 2, 2,1) + 2 (0, 2, 0,1) + 3 (-2, 0, -4,3) = (a, b, c, d ) .2 1 - 23 = a 21 + 2 2 = b : . : 21 - 4 3 = c 1 + 2 + 33 = d 1 2 , . C = 2 1 0 2 0 1 -2 0 -4 3 a b K c d 1 0 0 0 0 1 0 0 0 0 1 0 3a - b + 2d 3 -6a + 5b - 4d = C 6 -b + 2d 6 -2a + c v - a, b, c, d . 2a = c -2a + c = 0 . W - 1 , 2 , 3 : B - v ' .3 . [ v] B 3a - b + 2d 3 - 6a + 5b - 4d : B v = 6 -b + 2 d 6 .4 ,(' ) W - B A . (a, b, 2a, d ) B B A :' 3a - b + 2d 3 - v = 6a + 5b - 4d [ ]B 6 -b + 2 d 6 [ v1] B = [ (1, 0, 2, 0)] B 1 0 2 1 v v 2 = [ 2 ] B = [ (0, 2, 0,1) ] B = [ 3 ] B = [ (0, 0, 0,3) ] B = - 1 - 0 0 1 : 1 0 2 1 1 -2 - " , . M = 0 1 0 1 0 2 1 0 2 , . M = -1 1 -2 = 0 1 0 =* 1 0 : 0 0 1 0 0 1 - M . W - B A ,V.36 , . B A B ...
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