Addendum to “Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers” [J. Algebra 427 (2015) 20–29]
نویسندگان
چکیده
منابع مشابه
Matrix Theory over the Complex Quaternion Algebra
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex quaternion matrices, and so on. AMS Mathematics Subject Classification: 15A06; 15A24; 15A33
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NC algorithms are given for determining the number and degrees of the factors, irreducible over the complex numbers C, of a multivariate polynomial with rational coeÆcients and for approximating each irreducible factor. NC is the class of functions computable by logspace-uniform boolean circuits of polynomial size and polylogarithmic depth. The measures of size of the input polynomial are its d...
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The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
متن کاملAddendum to "Factoring polynomials over finite fields with Drinfeld modules"
After my paper [2] was electronically published by Mathematics of Computation, I came across the PhD thesis of professor I. Y. Potemine [6]. In Section 4.3 of his thesis, an algorithm for factoring polynomials is proposed which is equivalent to the algorithm discussed in my paper. Potemine’s algorithm is acknowledged in my PhD thesis [1]. Our algorithms were found independently, both as analogu...
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This document provides a mathematical summary of quaternion algebra and calculus and how they relate to rotations and interpolation of rotations. The ideas are based on the article [1].
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.06.014