This means that an nbyk matrix G is orthonormal if and only if
where G^{*} denotes the conjugate transpose of G and I_{k} is the kbyk identity matrix.
If the nbyk matrix G is orthonormal, then k ≤ n. The real nbyk orthonormal matrices are precisely the matrices that result from deleting nk columns from an orthogonal matrix; the complex nbyk orthonormal matrices are precisely the matrices that result from deleting nk columns from an unitary matrix. In particular, unitary and orthogonal matrices are themselves orthonormal.
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