This means that an n-by-k matrix G is orthonormal if and only if
If the n-by-k matrix G is orthonormal, then k ≤ n. The real n-by-k orthonormal matrices are precisely the matrices that result from deleting n-k columns from an orthogonal matrix; the complex n-by-k orthonormal matrices are precisely the matrices that result from deleting n-k columns from an unitary matrix. In particular, unitary and orthogonal matrices are themselves orthonormal.