.
m ´ n , mn (m n ):
Am´n = , aij ,
i = 1,2,, m , j = 1,2,, n .
, , .
:
1) : , ;
2) n = 1 -: X = ;
3) m = 1 -: Y = ;
4) m = n : An´n = .
( a 11 a nn) .
:
1) ( ,
, ):
E = ;
2) : ;
3) : .
, :
Am´n = Bm´n Û aij = bij (i = 1,2,, m; j = 1,2,, n).
A k:
B = k × A = ,
, :
B = k × A Û bij = k × aij (i = 1,2,, m; j = 1,2,, n). (21)
() A B :
Cm´n = Am´n Bm´n Û cij = aij bij (i = 1,2,, m; j = 1,2,, n). (22)
Am´n Bn´k:
Cm´k = Am´n × Bn´k
cij = ai1b1j + ai2b2j + ¼ + ainbnj (i = 1,2,, m; j = 1,2,, k). (23)
(23) , : Am´n Bn´k Cm´k, cij i- A j- .
. , .. .
,
,
, , . .
( ):
det A = = a 11 a 22 a 12 a 21. (24)
( ):
det A = (25)
: | A | Δ.
aij , i - j - ( Mij).
aij ( Aij) :
Aij = (1) i+j× Mij. (26)
, 1- :
|
|
, (27)
, :
,
.. . .