The covariance matrix belonging to this new S-base then is: 
(22) L co = (1 xor?«(S) 
If the null-space is known and the contraints-matrix has been chosen any S- 
transformation can be derived. 
REFERENCES 
1. Baarda. W. S-transformations and Criterion Matrices, Netherlands Geodetic 
Commission, Publications on Geodesy, New Series, Vol. 5, No. 1, 1973, Delft. 
2. Molenaar. M. A further inquiry into the Theory of S-transformations and 
Criterion Matrices, Netherlands Geodetic Commission, Publications on Geodesy, 
New Series, Vol. 7, No. 1, 1981, Delft. 
3. Teunissen, P.J.G. Generalized Inverses, Adjustment, The Datum Problem and 
S-transformations, Lecture Notes, International School of Geodesy, 3rd Course: 
Optimization and Design of Geodetic Networks, Erice-Trapani-Sicily, 25 April 10 
May 1984. 
4. Teunissen, P.J.G. The Geometry of Geodetic Inverse Linear Mapping and Non- 
Linear Adjustment, Netherlands Geodetic Commission, Publications on Geodesy, 
Vol. 9, No. 1, 1985, Delft. 
5. Tienstra. J. M. Theory of the Adjustment of Normally Distributed Observations, 
N.V. Uitgevery Argus, 1956, Amsterdam. 
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