This paper deals with new generalized inverses of rectangular complex matrices, namely 1MP and MP1-inverses. They are constructed from oblique projectors represented by means of inner generalized inverses, by using an adequate equivalence relation, and then passing to the quotient set. We give characterizations and general expressions for 1MP and MP1-inverses. As applications, the binary relations induced for these new generalized inverses are proved to be partial orders.

中文翻译：

---

从投影仪到 1MP 和 MP1 广义逆及其诱导偏序

本文处理矩形复矩阵的新广义逆矩阵，即 1MP 和 MP1 逆矩阵。它们由通过内部广义逆表示的斜投影构造，通过使用适当的等价关系，然后传递到商集。我们给出了 1MP 和 MP1 逆的特征和一般表达式。作为应用，这些新的广义逆的二元关系被证明是偏序的。