where gtd and Si are the weight coefficient and the weight matrix 
respectively of the observations. 
The relationship (1.4) can be interpreted as a linear transformation of 
; a 
the contravariant coordinates Ax} to the coordinates a with 
ve 
e 
respect to a new covariant base a 
e 
p 
Since the contravariant coordinates are transformed according to (1.4), 
the covariant base is transformed as /6/. 
le, =, 1 = [e,]% [a] aly (1.7) 
where Xx indicates transposition 
and the contravariant base as 
a a 
e u. 
1 
à 
= e 1.8 
; of [<7] (1.8) 
e u. 
i 
From these relationships and from (1.6), follows 
2a wu a 3.5 iade al L 
eg 7 ue "* Ag =u, 5; A57 u; Ag = 0 (1.9) 
Since the inner product in (1.9) is zero, the vectors e? and eg are 
perpedicular. Hence, the e,-space can be split into two perpendicular 
subspaces. One, spanned by the base vectors e? , and the other, by the 
base vectors eg 
The former, will be called condition space or in short e? -space and the 
latter, parameter space or eg "Space. 
The above process has been depicted in fig. 1 
- G60