Proving and Extending Greub-Reinboldt Inequality Using the Two Nonzero Component Lemma

Morteza Seddighin

Indiana University East, Richmond, IN 47374, USA.

DOI: 10.4236/alamt.2014.42010                

Abstract

We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequality becomes equality. Furthermore, using the Two Nonzero Component Lemma, we will generalize Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.

Keywords

Greub-Reinboldt Inequality, Two Nonzero Component Lemma

Conflicts of Interest

The authors declare no conflicts of interest.

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