Euclidean

adj

1. Alternative spelling of Euclidean.

   “If (#92;alpha#95;1,#92;dots,#92;alpha#95;n) is an orthonormal basis of a euclidean space V, then for all #92;alpha,#92;beta in V#92;alpha#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;i)#92;alpha#95;i#92;quad#92;text#123;and#125;#92;quad(#92;alpha#92;vert#92;beta)#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;i)(#92;beta#92;vert#92;alpha#95;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.”