- . m Ai, (i= 1, 2,...,m), - n j, (j= 1, 2,..., n). , mxn.
Ai Bj (i= 1, 2,...,m; j= 1, 2,..., n)
, .. aij ( ) (-aij) . . , aij (Ai,Bj).
=(aij), i=1,2,...,m; j=1,2,...,n, , Ai Bj, :
= .
Ai , - Bj . aij , Ai, Bj. (.., ).
1. . (I II). , , 1 . . , 1 . .
. .
1 I, 2 - II.
1 I, 2 - II.
I , .. (1,1), , .. 11=-1. 22=-1 ( (2,2). , (1,2) (2,1) 1 , 12=21=1. .. .
mxn =(aij) i= 1, 2,...,m; j= 1, 2,..., n 1,2,,m. i, (, ) , . ai i ( I- ). .. i ai = .
, , , .. aI (i=1,2,,m) : . a , (). .
.
i, , .
, . j , j- , .. £ . j, . . bj, j=1,2,..., n, bj, , .. , (). . ,
|
|
j, , .
, , . , , .
, (3) ( ), , , .
, , , , . ( ) n, ( ) n. , , .. , .
, , a=b=n, i, j. . , , .
2. ,
= .
. aij 0, 2, -1. =2. a=2 , A.
b ( ) . : 3, 2, 4, 5. , b = min {3; 2; 4; 5} = 2.
, a = b = v . A A2, 2; B B2, . ( A) ( B).