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.
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