We study degeneracies between cosmological parameters and measurement errors from cosmic shear surveys using a principal component analysis of the Fisher matrix. We simulate realistic survey topologies with non-uniform sky coverage, and quantify the effect of survey geometry, depth and noise from intrinsic galaxy ellipticities on the parameter errors. This analysis allows us to optimise the survey geometry. Using the shear two-point correlation functions and the aperture mass dispersion, we study various degeneracy directions in a multi-dimensional parameter space spanned by Omega_m, Omega_Lambda, sigma_8, the shape parameter Gamma, the spectral index n_s, along with parameters that specify the distribution of source galaxies. If only three parameters are to be obtained from weak lensing data, a single principal component is dominant and contains all information about the main parameter degeneracies and their errors. The variance of the dominant principal component of the Fisher matrix shows a minimum for survey strategies which have small cosmic variance and measure the shear correlation up to several degrees [abridged].
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