On the Algebraic Structure of Second Order Symmetric Tensors in 5-Dimensional Space-times

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is obtained. A theorem which collects together some basic results on the algebraic structure of the Ricci tensor in 5-dimensional space-times is also stated.