53. j , (, ) = ( j (), j ()). (49)
.
j .
10. | | = | j ()| .
| | = = = | j ()|.
20. = .
30. n , = (1, 2,..., n) , j . j () = ×, j () = ×, ; (, ) = ××, (j (), j ()) = (×)× ×(×) = ×( × × )× . (, ) = (j (), j ()), = × × . ,
= × × (50)
. n , , (48), .
= (1, 2,..., n) , = (50)
× = , = 1.
54. ,
= 1 (51).
48. , .
30 53.
49. , ( ) 1, ( ) .
51.
50. , .
. Þ j: n n = (1, 2,..., n) n. , . j () = × . ,
= . | j () = 11 + 22 + + nn. , (j ())2 = = ()2 = 1, .. j () . (j (), j ()) = 1×1 + 2×2 + + n×n = (, ) = 0, |
¹ , .. j () ^ j (). j () , , .. j () . , j () .
Ü j () . 1 = (j ())2 = 0 = (j (), j ()) = 1×1 + 2×2 + + n×n ¹ . , 49, .
51. , | | = 1.
|
|
, , × = . | × | = | |, | |×| | = 1, | |×| | = 1, | |2 = 1, | | = 1.
52. 1 (1).
. l j.
(1, 2, , n), × = l×, j. , . . . , . , . , .. | l |2 = 1. , 1 (1).
53. , .
. n (, ) = (j (), j ()) = (l1 , l2 ) = = l1l2 (, ). l1 ¹ l2, , , l1 =1, l2 = 1. , (, ) = (, ). (, ) = 0. , .