hence u must be a solution vector of (7) since it is a linear combination of vectors, 
defining the null-space of N (and A). 
Defining U as the solution space of u one may write: 
(10) u=D,,.teU 
So far U has been the solution space for the homogenious set of equations. 
What is the solution space V for the inhomogenious set of equations? 
From linear algebra it is known that V is a linear variety parallel to the solution 
space U which means that V equals one particular solution AX of (8) plus the 
solution space U, hence 
(11) V=(4X°)+U 
All solutions A X can be written as: 
21 
(12 AX- AX" « D^ t 
In least-squares adjustment problems one looks for a solution vector and not for a 
solution space. Therefore this solution space must be reduced to a one dimensional 
solution vector. This can be done by "constraining" the solution space. 
The constraints are: 
where B is a (pxm) constraints-matrix. 
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