-2 +6
o 2
(8)
5
e,=-K1
e2+^2
e3 K1
ei
e5= ^2
K
K.,
&n4
&n3 T~ K2
en—2 K1 -
&n1 A
en Ki
K,
K,
The matrix O" of the normal-equations (II, 4) becomes:
+6 2 oo
o
o
O
O
2 O
+6 2
+6 2 o
2 +6 2 o
0 2 +6 2
o 2 +6
It is symmetrical about both its diagonals.
B) The tensor of cofactors of the correlates and together with it
the solution of the normal-equations is directly given, if the special
properties of the matrix (8) are used.
The solution of the set of equations Gpa Kp t° is given by
GPO t° KP and the relation between Gp° and Gpa by the Kronecker
delta.
Ppc
According the theorem of Cramer is Gpa in which Tp°
represents the minor of G"° and A the value of the determinant
I G?°
The Gpa with equal indices are assumed to be equal, and also those
in which the relation 0 p 1 exists between the indices. The
Gpa o if 0 p 2. The rank of the determinant is b.
It can be proved that the elements of the first row of the inverse
matrix Gpo are:
A-G1i6= (G1-2) 1
(the sign is if b is an odd number)
Gh b—i P.Gh b
Gi, b-2 P-G1: b—i Gh b
Gh j__3 P.G1i b—2 Gh b—i etc. bi 1 inclusive
in which P and A G1'2 (P.Gj xGl 2).
G1'2
The elements of the second row are:
G2j b_1 P.G2: b
G2j b—2~P-G2, b—iG2y b etc. b i —2 inclusive.
