共轭四元数

The research of matrixes is continuously an important aspect of the quaternion division algebra. The purpose of this paper is to discuss the property of skew self-conjugate matrix. The definition of skew self-conjugate matrix on real quaternion division algebra is given.

四元数体上矩阵的研究是四元数代数理论中的一个重要方面，本文研究实四元数体上斜自共轭矩阵的性质，给出实四元数体上斜自共轭矩阵的定义。

Basing on the famous Schur theorem on real quaternion division algebra and the operation of matrix, some properties and judging criterions of skew self-conjugate matrix are obtained. Several theorems about characteristic value, similar decomposition and real expression of skew self- conjugate matrix are gained.

借助四元数体上的Schur三角分解定理和体上矩阵的运算，得到了斜自共轭矩阵的一些性质及判定准则，获得了斜自共轭矩阵的实表示、相似分解以及特征值的几个定理。

In this paper, we describe the history of Mizar system and the method to use theMizar system. Then we give the definition of quaternion numbers, module, algebrastructre etc, and then we prove its properties.

本文首先介绍了Miza(来源：ABC论文61网www.abclunwen.com)r系统的计算机操作原理和使用方法，给出了在Mizar语言系统下四元数、四元数的运算、共轭、内积、模等代数结构理论的证明，所做结论都通过了Mizar系统的验证，发表在波兰的《Formalized Mathematics》杂志上，并被收录到MML数据库中。

It is studied factorizing a matrix over quaternion field to the product of two self-conjugate matrices. And some useful results are obtained.

摘要研究了四元数矩阵分解为两个自共轭矩阵乘积，其中有一个是非奇异阵的条件，得到了一些有用的结果。

The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed.

讨论四元数Hermitian矩阵对在共轭合同关系下的同时对角化问题。

The conjugation by a unit quaternion (a quaternion of absolute value 1) with real part cos is a rotation by an angle 2''t'', the axis of the rotation being the direction of the imaginary part.

单位四元数（绝对值为1的四元数）若实部为 cos，它的共轭作用是一个角度为2''t''的转动，转轴为虚部的方向。

In this paper, some results of the self-conjugate matrices over skew-field of quaternions are given.

本文在[l—5]基础上，给出四元数自共轭矩阵若干结果。

A conclusion that the symmetric product of a self-conjugate matrix is still a self-conjugate matrix was obtained.

给出实四元数体上矩阵对称积的定义，得到了自共轭矩阵的对称积仍是自共轭矩阵的结论。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。