Translation Groups

Walter Benz
Additional contact information
Walter Benz: Universität Hamburg, FB Mathematik Mathematisches Seminar

Chapter Chapter 1 in Classical Geometries in Modern Contexts, 2012, pp 1-36 from Springer

Abstract: Abstract A real inner product space $$ (X,\delta) $$ is a real vector space X together with a mapping $$ \delta : X \times X \rightarrow \mathbb{R} $$ satisfying $$ {\rm(i)} \quad \delta\, (x,y)= \delta \,(y,x), $$ $$ {\rm(ii)}\quad\delta \,(x+y,z)= \delta \, (x,z)+ \delta(y,z), $$ $$ {\rm(iii)}\quad\delta \,(\lambda x,y)= \lambda \cdot\,\delta (x,y), $$ $$ {\rm(iv)}\quad\delta \, (x,x)>0 \,\, {\rm{for}} \,\, x \neq 0, $$ for all $$ x,y,z \,\in X $$ $$ \lambda \in \mathbb{R}$$ .

Keywords: Distance Function; Rational Number; Product Space; Real Vector Space; Hyperbolic Geometry (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0420-2_1

Ordering information: This item can be ordered from
http://www.springer.com/9783034804202

DOI: 10.1007/978-3-0348-0420-2_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().