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Zeros of quaternion polynomials. (English) Zbl 0979.30030
For each \(q \in \mathbb H\) let \([q]\) be the equivalence class of all elements \(q'\) having the form \(xqx^{-1}\) with some \(x \in \mathbb H\). Then the authors show that for a quaternionic polynomial of the form \(f(x) = (x - x_1)\dots (x - x_n)\) the subset \(\text{zero}(f) \cap [x_r]\) is nonempty for each \(r\). This leads to a computational method to determine the zeros of the polynomial.

30G35 Functions of hypercomplex variables and generalized variables
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
Full Text: DOI
[1] Zhang, F., Quaternions and matrices of quaternions, Lin. alg. and its appl., 251, 21-57, (1997) · Zbl 0873.15008
[2] Lam, T.Y., A first course in noncommutative rings, (1991), Springer Verlag, Chapter V, Section 16 · Zbl 0728.16001
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[4] Serodio, R.; Pereira, E.; Vitoria, J., Computing the zeros of quaternion polynomials, () · Zbl 1050.30037
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