The aim of this work is to characterize linear maps of infinite-dimensional inner product spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $Ain ext{Mat}_{nimes m} ({mathbb C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, the least norm solution of an infinite linear system from the Moore-Penrose inverse offered is studied.
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机译:这项工作的目的是表征无限尺寸内部产品空间的线性映射,其中莫雷猪糖逆转。此MP逆概括了矩阵$ a in text {mat} _ {n times m}({ mathbb c})$的众所周知的moore-penrose逆。此外,给出了对无限尺寸矢量空间上一些基因族的计算的方法。作为一种应用,研究了来自Moore-Penrose逆提供的无限线性系统的最低规范解。
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