The Pythagorean Theorem: I. The finite case

被引：51

作者：

Kadison, RV ^{[1
]}

机构：

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2002年 / 99卷 / 07期

关键词：

D O I：

10.1073/pnas.032677199

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both "discrete" and "continuous.".

引用

页码：4178 / 4184

页数：7