论文标题
P-canonical形式和完整的反转
P-canonical forms and complete inverses
论文作者
论文摘要
本文将联想环中元素的一种新型反向描述为完全的逆，是一组方程组的独特解决方案。当$ a $ $ a $的情况下，仅当存在$ a $的逆向时，这种逆。我们还表明，通过插入$ -k $ for $ k $中的$ \ Mathcal {p} $ - 正方形矩阵$ a $的规范形式，我们得到了$ \ Mathcal {p} $ - $ a $ a $的完全倒数的规范形式。
This paper describes a new kind of inverse for elements in associative ring, that is the complete inverse, as the unique solution of a certain set of equations. This inverse exists for an element $a$ if and only if the Drazin inverse of $a$ exists. We also show that by plugging in $-k$ for $k$ in the $\mathcal{P}$-canonical form of a square matrix $A$, we get the $\mathcal{P}$-canonical form of the complete inverse of $A$.
