广义四元数矩阵方程 AX -DXB =R(英文)

设 HF 为域 F上的广义四元数除环 ,Ch F≠ 2 .本文利用拟线性变换 T(X) =AX - DXB讨论HF 上矩阵方程 AX - DXB =R的求解问题 ,获得了上方程存在 (唯一 )解的几个充分必要条件 ,并给出了解的显式公式 .

一类广义延拓四元数矩阵的奇异值分解

从普通四元数矩阵的奇异值分解出发,给出了具有行或列对称结构的一类四元数矩阵(即广义四元数延拓矩阵)的奇异值、奇异向量与其母矩阵的奇异值、奇异向量之间的定量关系,推广了现有文献的结果。理论分析和数值实验的结果表明,就一大类广义四元数延拓矩阵而言,仅用母矩阵进行奇异值分解不但可以节省计算量和存储量,而且不影响任何数值精度。

四元数矩阵的线性表示

分别给出了四元数矩阵的一种新的复表示矩阵以及广义四元数矩阵的线性表示.

On the First-degree Algebraic Equation of the Generalized Quaternion

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.

An Equality for Trace of Matrix over a Generalized Quaternion Algebra

The well-known trace equality of similar matrices does not necessarily hold for matrices over non-commutative algebras and rings. An interesting question is to give conditions such that trace equality of similar matrices holds for matrices over a non-commutative algebra or ring. in this note, we show that for any two matrices A and B over a generalized quaternion algebra defined 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 F, then their traces are equal.