euclidean

See also: Euclidean

English

Pronunciation

• Rhymes: -ɪdiən

Adjective

euclidean (not comparable)

1. (rare) Alternative spelling of Euclidean
   • 1968, Robert R. Stoll, Edward T. Wong, Linear Algebra, London: Academic Press, →LCCN, page 76:

     If $(\alpha _{1},\dots ,\alpha _{n})$ is an orthonormal basis of a euclidean space $V$, then for all $\alpha ,\beta$ in $V$

     $$\alpha =\sum _{i=1}^{n}(\alpha \vert \alpha _{i})\alpha _{i}\quad {\text{and}}\quad (\alpha \vert \beta )=\sum _{i=1}^{n}(\alpha \vert \alpha _{i})(\beta \vert \alpha _{i}).$$

     We turn now to a somewhat more profound matter. Suppose that we partially order by inclusion the collection of all orthonormal sets of vectors in a euclidean space $V$. A maximal element of this set is called a maximal orthonormal set.