Inequalities for generalized minors

TL;DR

This paper extends classical bounds on matrix minors to the setting of Jordan pairs, providing new inequalities involving generalized minors and Jordan algebra determinants.

Contribution

It generalizes known inequalities for matrix minors to the broader context of Jordan pairs and their determinants, expanding the theoretical framework.

Findings

Established bounds for generalized minors in Jordan pairs.

Connected classical matrix inequalities to Jordan algebra theory.

Provided a foundation for further research in Jordan algebra inequalities.

Abstract

It is a classical result that the absolute value of any $k$-minor of an $r\times s$ real or complex matrix is bounded by the product of its first $k$ singular values. We generalize this statement to the context of real or complex simple Jordan pairs with generalized minors given by Jordan algebra determinants.