Sentence examples for be a root vector from inspiring English sources
Let ({f in mathbb{K}[z]}) be a polynomial of degree ({n ge2}), ({xiin mathbb{K}^{n}}) be a root vector of f and ({N ge0}).
Let ({f in mathbb{K}[z]}) be a polynomial of degree ({n ge2}), ({xiin mathbb{K}^{n}}) be a root vector of f and ({1 le p leinfty}).
Let ({f in mathbb{K}[z]}) be a polynomial of degree ({n ge2}) which has only simple zeros in (mathbb{K}), and let ({xiin mathbb{K}^{n}}) be a root vector of f.
Let ({f in mathbb{K}[z]}) be a polynomial of degree ({n ge2}) which has only simple zeros, ({xiin mathbb{K}^{n}}) be a root vector of f and ({1 le p leinfty}).
Let ({f in mathbb{C}[z]}) be a polynomial of degree ({n ge2}) which has only simple zeros, ({xiin mathbb{C}^{n}}) be a root vector of f and ({N ge1}).
Let ({f in mathbb{K}[z]}) be a polynomial of degree ({n ge2}) which has only simple zeros in (mathbb{K}), ({xiin mathbb{K}^{n}}) be a root vector of f, ({N ge0}), and ({1 le p leinfty}).
Thus, ({u_{k},v_{ k} mid kinLambda}) is a root vector system of the Hamiltonian operator matrix H.
It follows from Lemma 4.5, Lemma 4.3 v), and Lemma 2.3 that E is a function of the initial conditions of (T^{(N }) with a strict gauge function (varphi_{N}) of order ({r = 2 N + 1}) on J. Since ξ is a root vector of f, then ({E xi) = 0 in J}).
It follows from Theorem 6.2 that if there exists an integer ({m ge0}) such that E_{f}bigl(x^{(m)}bigr) lemathscr{R} = frac{8}{(3 + sqrt{8 n - 7})^{2}}, (7.3) then f has only simple zeros and the Ehrlich-type iteration (1.18) is well defined and converges to a root vector ξ of f with order of convergence ({2N + 1}).
(6.9) Then f has only simple zeros in (mathbb{K}) and the Ehrlich-type iteration (1.18) is well defined and converges to a root vector ξ of f with order of convergence ({2N + 1}) and with error estimate (6.6) for ({p = infty}).
