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.