TY - CONF AB - 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 the size of the matrix' spectrum (=number of different eigenvalues) is known in advance, it can be diagonalized effectively. Thus, in principle the spectral decomposition can be computed under remarkably weak non-degeneracy conditions. AU - Ziegler, Martin AU - Brattka, Vasco ID - 18152 SN - 0302-9743 T2 - Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA'2000) TI - A Computable Spectral Theorem VL - 2064 ER -