Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1,1…1], [21…1], [31\ldots 1], [z\bar{z}1…1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.