标题： 线性四元数函数的规范形式 显示英文标题

标题： Canonic form of linear quaternion functions

摘要： 一次阶的一般线性四元数函数是带有左侧和右侧四元数系数的项的和。 本文考虑了此类函数的规范形式，并基于Todd Ell的最新工作，他已证明任何此类函数最多可以使用四个四元数系数来表示。 在本文中，提出了一种新的简单方法，使用矩阵方法数值地获得这些系数，该方法也给出了规范形式的另一种证明。 显示英文摘要

摘要： The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown that any such function may be represented using at most four quaternion coefficients. In this paper, a new and simple method is presented for obtaining these coefficients numerically using a matrix approach which also gives an alternative proof of the canonic forms.