A, X, dim(x)=n e1, e2,..., en - X. A e1 = (a11,...,an1),..., A en = (a1n,...,ann) e1, e2,..., en.
, .
, , n- , n; - n , .
, y = A x X, , , A.
, , . X e = {e1,..., en} e' = {e'1,..., e'n}. Ae A e Ae' e'
- e e' .
, , :
1. + = +.
2. ( +) + = + ( + ).
3. + = .
4. () + = .
:
1. ) = ( ).
2. () = ().
3. ( + ) = + , ( + ) = + .
, , :1. = ; 0 = ; (1)= . 2. β ) .3. = + β . 4. ( + ) = + .
28 . . .
, R , R R.
9.1. , λ :
( + )= + , (λ ) = λ . (9.1)
9.2. , .
: = .
1, 2, 3, . , 1, 2, 3, . , :
1 = 11 1 + 21 2 +31 3,
2 = 12 1 + 22 2 + 32 3, (9.2)
3 = 13 1 + 23 2 + 33 3.
1, 2, 3 . (9.2) .
. , .
|
|
=1 1 + 2 2 + 3 3 , : =`1 1 + `2 2 + `3 3, x`i :
`1 = a11x1 + a12x2 + a13x3,
x`2 = a21x1 + a22x2 + a23x3, (9.3)
x`3 = a31x1 + a32x2 + a33x3.
.