# A Computable Spectral Theorem

@inproceedings{Ziegler2000ACS, title={A Computable Spectral Theorem}, author={Martin Ziegler and Vasco Brattka}, booktitle={CCA}, year={2000} }

Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation's effectivity properties on the sound formal basis of computable analysis. It turns out that in general the eigenvectors cannot be computed from a given matrix. If however…

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