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Algebraic theory of generalized inverses

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraic theory of generalized inversesby Jianlong Chen, Xiaoxiang Zhang.
Author:	Chen, Jianlong.
other author:	Zhang, Xiaoxiang.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	xi, 322 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Matrix inversion.
Online resource:	https://doi.org/10.1007/978-981-99-8285-1
ISBN:	9789819982851$q(electronic bk.)

Algebraic theory of generalized inverses
Chen, Jianlong.

Algebraic theory of generalized inverses[electronic resource] /by Jianlong Chen, Xiaoxiang Zhang. - Singapore :Springer Nature Singapore :2024. - xi, 322 p. :ill., digital ;24 cm.

Preface -- Algebraic Basic Knowledge -- Moore-Penrose Inverses -- Group Inverses -- Drazin Inverses -- Core Inverses -- Pseudo Core Inverses -- Bibliography -- Index.

Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases. In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalized inverses of elements in rings and semigroups, as well as morphisms in categories. The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system. Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book helpful.

ISBN: 9789819982851$q(electronic bk.)

Standard No.: 10.1007/978-981-99-8285-1doiSubjects--Topical Terms:

345297
Matrix inversion.

LC Class. No.: QA188

Dewey Class. No.: 512.9434

Algebraic theory of generalized inverses
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505 0 $a Preface -- Algebraic Basic Knowledge -- Moore-Penrose Inverses -- Group Inverses -- Drazin Inverses -- Core Inverses -- Pseudo Core Inverses -- Bibliography -- Index.
520 $a Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases. In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalized inverses of elements in rings and semigroups, as well as morphisms in categories. The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system. Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book helpful.
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