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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