Trace minimization principles for positive semi-definite pencils (Q1940103)

The authors, for a given (regular or singular) Hermitian matrix pencil \(A-\lambda B\) of order \(n\), are interested in when \(\inf_{X^HAX=J_k}\mathrm{trace}(X^HAX)\) is finite and attainable. First, in the introduction, they present the problem and they refer to previously established results from other authors, especially for the case of \(B\) being a non singular matrix. In the next two sections, they provide and prove their main results. Finally, in the fourth section, they prove a sufficient and necessary condition for infimum attainability.