Evenness of the Jordan structure of block quaternions with real spectra and its computational consequences (Q1975113)

The author shows that the block quaternion is an even order complex matrix of a special block form. It has been known that, if such a matrix has a real eigenvalue, then its algebraic multiplicity is even. It is proved that a stronger property is valid: The whole part of the Jordan structure associated with the real eigenvalues of a block quaternion is even. This implies that the number of Jordan blocks associated with a real eigenvalue is even. The consequences of this property related to the numerical solution of eigenvalue problems for block quaternions are discussed.