论文标题
Clifford代数$ C \ ell_ {1,2} $的Moore-Penrose倒置
The Moore-Penrose Inverses of Clifford Algebra $C\ell_{1,2}$
论文作者
论文摘要
在本文中，我们在Clifford代数$ C \ ell_ {1,2} $和一个矩阵环之间介绍了戒指同构。通过这样的戒指同构，我们介绍了Clifford代数$ C \ ell_ {1,2} $中Moore-Penrose逆的概念。使用Moore-Penrose倒数，我们求解线性方程$ axb = d $ in $ c \ ell_ {1,2} $。我们还获得了$ c \ ell_ {1,2} $中两个数字的必要条件，以使其相似。
In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_{1,2}$ and a ring of matrices. By such a ring isomorphism, we introduce the concept of the Moore-Penrose inverse in Clifford algebra $C\ell_{1,2}$. Using the Moore-Penrose inverse, we solve the linear equation $axb=d$ in $C\ell_{1,2}$. We also obtain necessary and sufficient conditions for two numbers in $C\ell_{1,2}$ to be similar.
