Let A, B be two square matrices with complex coefficients, of respective orders n and m, where n ≥ m. We shall say that B is imbeddable in A if there exists a unitary matrix U of order n such that U*AU contains B a s a principal submatrix. In other words, B is said to be imbeddable in A if there exists a matrix V of type n × m such that V*V = IW (= the identity matrix of order m) and V*AV = B.