Isometric embeddings of metric \(Q\)-vector spaces into \(Q^N\) (Q1272772)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Isometric embeddings of metric \(Q\)-vector spaces into \(Q^N\) |
scientific article; zbMATH DE number 1235000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isometric embeddings of metric \(Q\)-vector spaces into \(Q^N\) |
scientific article; zbMATH DE number 1235000 |
Statements
Isometric embeddings of metric \(Q\)-vector spaces into \(Q^N\) (English)
0 references
3 January 1999
0 references
Let \(Q\) be the field of rationals and \(W\) an \(n\)-dimensional Euclidean vector space over \(Q\). The author proves that \(W\) is isometrically embeddable in \(Q^{n+3}\) and gives an explicit algorithm for obtaining the minimum \(N\) such that \(W\) is isometrically embeddable in \(Q^N\). This answers open problems posed by \textit{H. Maehara} [Embedding a set of rational points in lower dimensions, to appear is Discrete Math. 192, 273-279 (1998; Zbl 0956.51009)].
0 references
isometric embeddings
0 references
metric \(Q\)-vector spaces
0 references
algorithm
0 references
