算子的加权 1MP 和 MP1 逆运算

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-05-28 DOI:10.1515/ms-2024-0033

Dijana Mosić, Janko Marovt

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引用次数: 0

摘要

本文的主要目的是扩展为矩形复矩阵定义的 1MP 和 MP1 逆的概念。我们提出了两个希尔伯特空间之间有界线性算子的加权 1MP 和 MP1 逆，作为两种新的广义逆。加权 1MP 和 MP1 逆的概念在矩形复矩阵中也是新的。我们建立了加权 1MP 和 MP1 逆的一些特征和表示。我们应用加权 1MP 和 MP1 反演求解了几个算子方程。其中一个方程的特例是与最小二乘法求解相关的正则方程。根据我们的结果，我们获得了 1MP 和 MP1 逆的新特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Weighted 1MP and MP1 inverses for operators

The main aim of this paper is to extend the concepts of the 1MP and MP1 inverses defined for rectangular complex matrices. We present the weighted 1MP and MP1 inverses for a bounded linear operator between two Hilbert spaces as two new kinds of generalized inverses. The notions of the weighted 1MP and MP1 inverses are new in the context of rectangular complex matrices too. We establish a number of characterizations and some representations of the weighted 1MP and MP1 inverses. Several operator equations are solved applying the weighted 1MP and MP1 inverses. A special case of one of these equations is the normal equation which is related with the least-squares solution. As consequences of our results, we obtain new properties of the 1MP and MP1 inverses.

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.