1) generalized quaternion
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广义四元数
1.
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
本文运用广义四元数代数的矩阵表示讨论了两类广义四元数的一次代数方程的解问题 ,并得到了这两类代数方程有唯一解、无穷多解、无解的判别条件。
2) generalized quaternion algebra
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广义四元数代数
1.
In this note, we show that for any two matrices A and B over a generalized quaternion algebra denned on an arbitrary field F of characteristic not equal to two, if A and B are similar and the main diagonal elements of A and B are in.
本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等。
3) generalized quaternion groups
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广义四元数群
1.
This paper perfectly resolves the CI property,normality and arc-transitive property of connected Cayley graphs of valencies 4 and 5 on generalized quaternion groups Q4pm(p is odd prime,m is positive integer).
完整解决了广义四元数群Q4pm(p为奇素数,m为正整数)的连通4度及5度无向Cayley图的CI性、正规性和弧传递性。
4) generalized quaternion group
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广义四元数群
1.
A group G is said to be a generalized quaternion groups,if Q4 n =<a,b│a2n=1,b2=an.
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一个有限群称为广义四元数群,若Q4n=,n≥3。
2.
A group G is said to be a generalized quaternion groups,if Q_(4p)=〈a,b|a~(2n)=1,b~2=a~n,a~b=a~(-1)〉,p3.
一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3。
5) Generalized quaternion matrix
![点击朗读](/dictall/images/read.gif)
广义四元数矩阵
6) generalized quaternion field
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广义四元数体
1.
This paper gives the structure formulas of the minimal polynomial and minimalcentral poiynomial of any nx n matrix over the generalized quaternion field,discusses their someproperties and applications,and obtalns a necessary and sufficient condition that a generalizedquaternion square matrix is similar to a diagonal matrix.
本文给出了广义四元数体上方阵的最小多项式与最小中心多项式的构造公式,讨论了它们的性质及其应用,得到广义四元数方阵相似于对角矩阵的一个充要条件。
补充资料:四元数
四元数 quaternions 数的一种。1843年英国数学家W.R.哈密顿为解决建立三维复数空间的问题,把复数x+iy作为一对有序偶的实数来研究,并定义了一套运算规则,使虚数i在复数运算中有了明确的意义。为此,他创立了有4个分量的新数,即t+xi+yj+zk,他把这个数称之为四元数。其中t为四元数的数量部分,也称纯量部分,xi+yj+zk为向量部分,式中i、j、k满足: i2=j2=k2=-1,ij=k,ji=-k,ki=j,ik=-j,jk=i,kj=-i。 四元数的建立为向量代数和向量分析奠定了基础,四元数系又构成了以实数域为系数域的有限维可除代数,从而促进了代数学的发展。 |
说明:补充资料仅用于学习参考,请勿用于其它任何用途。
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