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Spectral decomposition of matrices is a recurring and important task inapplied mathematics, physics and engineering. Many application problems requirethe consideration of matrices of size three with spectral decomposition overthe real numbers. If the functional dependence of the spectral decomposition onthe matrix elements has to be preserved, then closed-form solution approachesmust be considered. Existing closed-form expressions are based on the use ofprincipal matrix invariants which suffer from a number of deficiencies whenevaluated in the framework of finite precision arithmetic. This paperintroduces an alternative form for the computation of the involved matrixinvariants (in particular the discriminant) in terms of sum-of-productsexpressions as function of the matrix elements. We prove and demonstrate bynumerical examples that this alternative approach leads to increased floatingpoint accuracy, especially in all important limit cases (e.g. eigenvaluemultiplicity). It is believed that the combination of symbolic algorithms withthe accuracy improvements presented in this paper can serve as a powerfulbuilding block for many engineering tasks.

Symbolic spectral decomposition of 3x3 matrices