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