Abstract
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.
Acknowledgements
We wish to thank the referee for pointing out reference Citation20 and raising (converse) questions which resulted in Section 5.