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Let $A$ be a nonzero complex matrix $n \times n, x_0\in V_n(C), x_0\neq\Theta$. Let us define $x_k=A^kx_0$, $\mu_k=x^H_kx_k/x^H_{k-1}x_{k-1}$ and $v_k=x^H_{k-1}x_k/x^H_{k-1}x_{k-1}$. In this paper, assymptotic behaviour of the numbers $\mu_k$ and $v_k$ is studied in detail, mainly for matrices with nonlinear elementary divisors.
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