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Erschienen in:
2006 | OriginalPaper | Buchkapitel
On the Spectrum of Geodetic Networks
Erschienen in: Mathematical Foundation of Geodesy
Verlag: Springer Berlin Heidelberg
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The spectrum of a geodetic network is defined as the eigenvalues of the matrix
A
T
A
of normal equations corresponding to the observation equations
Ax
=
b
in the coordinates.
We find the meaning of and some general properties for the eigenvectors of the symmetric matrices
A
T
A
and
AA
T
and some results concerning the distribution of the eigenvalues when the network is relatively large.
The ultimate goal for these investigations is to get a deeper insight into the relations between netform and netquality. Unfortunately the results are rather fragmentary because we have only recently arrived at what we consider the core of the problem after years of research.