The Pythagorean Theorem: I. The finite case
- 2 April 2002
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 99 (7) , 4178-4184
- https://doi.org/10.1073/pnas.032677199
Abstract
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.”Keywords
This publication has 1 reference indexed in Scilit:
- Means and convex combinations of unitary operators.MATHEMATICA SCANDINAVICA, 1985