Abstract

The Fiedler's determinantal inequality stated by M. Fiedler in [5] (1971) provides bounds for the determinant of the sum of two Hermitian matrices. In this note, we extend the Fiedler's result to Euclidean Jordan algebras. In our proof, we use the commutation principle for variational problems which was recently introduced in these algebras. As an application, we obtain some Minkowski-type determinantal inequalities in Euclidean Jordan algebras.