Application of the Two Nonzero Component Lemma in Resource Allocation

Seddighin, Morteza

doi:10.4236/jamp.2014.27072

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“…Furthermore, he applied TNCL to solve some optimization problems in statistics, econometrics, and resource allocations. Please see [5]- [11]. Although this Lemma is implicitly used in all of the author's earlier papers up to 2008, it was not until 2008 that he stated a formal description of the Lemma in his paper titled, "Antieigenvalue Techniques in Statistics."…”

Section: Introductionmentioning

confidence: 99%

Two Nonzero Component Lemma and Matrix Trigonometry

Seddighin¹

2017

ALAMT

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In this paper we show that the author's Two Nonzero Lemma (TNCL) can be applied to present a simple proof for a very useful equality which was first proved by Karl Gustafson in 1968. Gustafson used Hilbert space methods, including convexity of the Hilbert space norm, to prove this identity which was the basis of his matrix trigonometry. By applying TNCL, we will reduce the problem to a simple problem of ordinary calculus.

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Section: Introductionmentioning

confidence: 99%