. , : 1, 2, 3, 4; 1, 2, 3, 4. , : b1 ; b2 ; b3 . 1, 2, 3, 4 , ( ) , aij (i = 1, 2, 3, 4, j = 1, 2, 3) - ; , (, , ).
1 | a11 | a12 | a13 |
2 | a21 | a22 | a23 |
3 | a31 | a32 | a33 |
4 | a41 | a42 | a43 |
( 1, 2, 3, 4, ), , .
. 1, 2, 3, 4 1, 2, 3, 4, . , , ( L); 1, 2, 3, 4:
L= 11+ 2 2+ 3 3+ 4 4,
, ,
,
, . , , . , 1 a11 , 1 - a11 1 , 2 1 a21 2 .., :
, 1, 2, 3, 4.
, : 1, 2, 3, 4,, :
U1, U2, U3. , b1 U1, b2 U2 b3 U3. , ; : β1, β2, β3 . - ; s1, s2, s3,, s4, γ1, γ2, γ3, γ3 . , . aij s1 (i = 1, 2, 3, 4), Uj (j = 1, 2, 3). aij , . aij ().
|
|
U1 | U2 | U3 | |
s 1 | a11 | a21 | a31 |
s 2 | a12 | a22 | a32 |
s 3 | a13 | a23 | a33 |
s 4 | a14 | a24 | a34 |
U1 1, U2 2, U3 3. ( ), ( ), .
. 1, 2, 3 U1, U2, U3, . -:
() -:
, . -:
, (1, 2, 3),
L= 11+ 2 2+ 3 3.
, : 1, 2, 3,, :
.
( )
, m, n . i (i = 1,, m) i ≥0, j- (j = 1,, n) bj ≥0. , , m×n, (ij) Ai Bj. ():
bj i | B1 | B2 | Bn | |||||
A1 | c11 | c12 | c1n | a1 | ||||
A2 | c21 | c22 | c2n | a2 | ||||
Am | cm1 | cm2 | cmn | am | ||||
b1 | b2 | bn |
i ( ai), j ( bj). ( , ) i j .
m×n:
.
ij :
1) :
(*)
2) :
(**)
|
|
3) :
i bj. , ,
,
( , ). , , (*) (**) .
, . :
:
:
, (m+n) ×mn. m+n-1, m+n-1 .