Hyperorthogonal family of vectors and the associated Gram matrix

Abstract

A family of non-zero vectors in Euclidean $n$-space is termed hyperorthogonal if the angle between any two distinct vectors of the family is at least $\pi /2$. Any hyperorthogonal family is finite and contains at most $2n$ vectors. It decomposes uniquely into the union of mutually orthogonal irreducible subfamilies. An equivalent formulation in terms of the associated Gram matrix is given.