Melania Moldovan, University of Maryland, Baltimore County


Strict diagonal dominance and a Gersgorin type theorem in Euclidean Jordan algebras


Abstract: For complex square matrices, the Levy-Desplanques theorem asserts that a strictly diagonally dominant matrix is invertible. The well-known Gersgorin theorem on the location of eigenvalues is equivalent to this. By describing the real/spectral eigenvalues of square Hermitian quaternionic matrices and 3 by 3 Hermitian octonionic matrices, we show how to extend the Levy-Desplanques theorem to an object in a Euclidean Jordan algebra when its Peirce decomposition with respect to a Jordan frame is given. As a consequence, we present a Gersgorin type theorem for the spectral eigenvalues of an object in a Euclidean Jordan algebra.

Advisors: Dr. M. Seetharama Gowda (University of Maryland, Baltimore County)