论文标题
Clifford代数$ C \ ELL_2 $的Moore-Penrose倒置
The Moore-Penrose Inverses of Clifford Algebra $C\ell_2$
论文作者
论文摘要
在本文中，我们在Clifford代数$ C \ ell_2 $和一个矩阵环之间介绍了一个戒指同构，并用Real Matrices表示元素。通过这样的戒指同构，我们在Clifford代数$ C \ ELL_2 $中介绍了Moore-Penrose逆的概念。我们解决线性方程$ axb = d $，$ ax = xb $和$ ax = \ bar {x} b $。我们还获得了$ c \ ell_2 $中两个数字的必要条件，并且具有相似性和伪造性。
In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_2$ and a ring of matrices, and represent the elements in $C\ell_2$ by real matrices. By such a ring isomorphism, we introduce the concept of the Moore-Penrose inverse in Clifford algebra $C\ell_2$. we solve the linear equation $axb=d$, $ax=xb$ and $ax=\bar{x}b$. We also obtain necessary and sufficient conditions for two numbers in $C\ell_2$ to be similar and pseudosimilar.
