L n n- , j: Ln Ln .
40. j, j () = l× l Î . l j.
, j Û $ l Î : j () = l× . , × = l× . × (l) × = , ( l)× = . , j Û ( l)× = (38). ( l) . (38) . ,
(39) | j Û (1, 2, , n) (39), . (39) , , , .. |
(40) | (340). (40) . , .. | l |, . |
. ( ). .
40, l Î . l0 Î . l0 (39) , . . j l0 j, .
37. .
. = 1××. l , | l | = | 1×× l | = | 1×× 1 × (l)× | = | 1× ( l)× | = | 1 || l || | = | l |.
,
. .
41. - .
38. j: Ln Ln, , , , .
.
.
1. .
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2. , (.. ).
3. l0 , .
. j: L4 L4 ( R), = ( 1, 2, 3, 4) .
= . | . (*). , , : | (*) |
, [(1 l)2 1]×[(1 l)×(3 l) 6] = 0. :
1) (1 l)2 1 = 0, 1 l = 1. l1 = 0, l2 = 2.
2) (1 l)×(3 l) 6 = 0, l2 4 l 3 = 0, l3 = , l4 = . , , . . .
1) l = 0. | 2 = 1. , |
, 4 = , 3 = . 1 = 3 , 2 = 3 , 3 = 13 , 4 = 11 , , . , , l = 0, (3 , 3 , 13 , 11 ).
2) l = 2. | 2 = 1. . |
, 3 = , 4 = 1 = 7 , 2 = 7 , 3 = 15 , 4 = 11 , . , , l = 2, (7 , 7 , 15 , 11 ).
3) l = . | 1 = 2 = 0. , |
, 3 . 3 = 2 , . , , l = 2 + , (0, 0, 2 , ). | |
4) l = . | 1 = 2 = 0. , |
, 3 . 3 = 2 , . , , l = 2 + , (0, 0, 2 , (1 ) ). |
.
10. j, l a ¹ 0, a× , .
j () = l , j (a ) = aj () = a (l ) = l (a ).
20. j: Ln Ln, ( ), Ln.
j () = l , j () = l . j (a + b ) = aj () + bj () = a (l ) + b (l ) = l (a + b ).
30. , , .
j () = l , j () = l1 , l ¹ l1. , = a . , a ¹ 0. j () = j (a ). l1 = a(l ), l1(a ) = a(l ), a (l1 l) = 0. a ¹ 0, l1 l ¹ 0, ¹ 0. . , .
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40. = (1, 2,..., , , n) j, l, - , -, = l.