Advances in Linear Algebra & Matrix Theory

Volume 7, Issue 1 (March 2017)

ISSN Print: 2165-333X   ISSN Online: 2165-3348

Google-based Impact Factor: 0.33  Citations  

Two Nonzero Component Lemma and Matrix Trigonometry

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DOI: 10.4236/alamt.2017.71001    1,589 Downloads   2,164 Views  
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ABSTRACT

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.

Cite this paper

Seddighin, M. (2017) Two Nonzero Component Lemma and Matrix Trigonometry. Advances in Linear Algebra & Matrix Theory, 7, 1-6. doi: 10.4236/alamt.2017.71001.

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