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

• 作者: Morteza Seddighin
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Greub-Reinboldt INEQUALITY TWO Nonzero COMPONENT LEMMA
• 年，卷（期）: 2014,（2）
• 页码范围: 120-127
• 页数: 8页
• 分类号: O1

摘要

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.