The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences
M. Seetharama Gowda, Jiyuan Tao · Linear and Multilinear Algebra · 2010
In this article, based on the min–max theorem of Hirzebruch, we formulate and prove the Cauchy interlacing theorem in simple Euclidean Jordan algebras. As a consequence, we relate the inertias of an element and its principal components and extend some well-known matrix theory theorems and inequalities to the setting of simple Euclidean Jordan algebras.