m n
:
AX = B,
A aij .
m = n A , A - 1,
A - 1 AX = A - 1 B
A − 1 A E ( ).
X = A - 1 B.
, .
aij A, bij B.
:
A λ (: λ A) B, A , B
bij = λ aij
A + B C, A B, C
cij = aij + bij
A − B , C,
cij = aij - bij
.
Θ , A A,
A + Θ = A
.
:
(: AB, ) C, .
cij = | ∑ | aikbkj |
k |
, . A , B , AB = C . .
. .
(: AT) , ,
A , AT
, .
E ( ) , ,
EA = AE = A
,
. A - 1 , , :
|
|
AA − 1 = E
. , , ( ), ( ). , () . () . () () . , .
1. A + (B + C) = (A + B) + C
2. A + B = B + A
3. A (BC) = (AB) C
4. A (B + C) = AB + AC
5. (B + C) A = BA + CA
6.
7.
8.
9. (AT) T = A
10. (A * B) T = BT * AT
, :
, .