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

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

     

     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 ${\displaystyle V}$. A maximal element of this set is called a maximal orthonormal set.