Trigonometry in complex inner product spaces

被引：0

作者：

Albahboh, Hussin ^{[1
]}

Gingold, Harry ^{[1
]}

Quaintance, Jocelyn ^{[2
]}

机构：

[1] West Virginia Univ, Dept Math, Morgantown, WV 26506 USA

[2] Univ Penn, Dept Comp Sci, Philadelphia, PA 10104 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 575卷

关键词：

Inner product space; Complex Hilbert space; Angle; Similarity; Trigonometry; Trigonometric formulas; Sine theorem; Cosine theorem; ANGLES;

D O I：

10.1016/j.laa.2019.04.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We adopt an appropriate definition of an angle in a Hilbert space over the complex field. It serves as a main tool for the enhancement of geometry and trigonometry of complex inner product spaces. A "sine theorem" is shown to hold based on which similarity theorems are proven. Trigonometric identities are shown to hold that lead to a main result that the sum of angles in a "triangle" in a complex Hilbert space is pi. Examples are given. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：216 / 234

页数：19

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