Quaternion Generalized Inverses

Foundations, Theory, Problems, and Solutions

Ivan I. Kyrchei (Autor)

Buch | Softcover

592 Seiten

2025
Academic Press Inc (Verlag)
978-0-443-34145-8 (ISBN)

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A cornerstone of linear algebra, the determinant's utility in real and complex fields is undeniable, though traditionally limited to invertibility, rank, and solving linear systems. Quaternion Generalized Inverses: Foundations, Theory, Problems, and Solutions ventures into uncharted territory: extending these concepts to linear algebra over the noncommutative quaternion skew field. The author's groundbreaking theory of "noncommutative" row–column determinants is central to this exploration, a significant advancement beyond the Moore determinant. This seven-chapter work thoroughly introduces the history of noncommutative determinants before delving into the author's theory and its application to inverse matrix computation and Cramer's rule for quaternion systems. The main portion of this work is dedicated to a comprehensive examination of quaternion generalized inverses, spanning the well-established Moore–Penrose and Drazin inverses to more recent developments such as core-EP and composite inverses. The book provides their definitions, properties, and, uniquely, their determinantal representations based on the author's noncommutative determinants. It culminates in demonstrating their powerful applications in solving a wide range of quaternion matrix equations, including Sylvester-type and constrained equations, as well as differential matrix equations.

Ivan I. Kyrchei is a leading researcher at the Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS, Ukraine. In 2008, he completed his PhD at the Taras Shevchenko National University (Kyiv, Ukraine). His dissertation developed the theory of column-row determinants of matrices over quaternion algebras, which are a generalization of Moore's determinant, previously introduced only for Hermitian matrices. These scientific interests have led to academic publications in about 100 scientific works and SCI papers, among them, Applied Mathematics and Computation, Linear Algebra and its Applications, Linear and Multilinear Algebra, Discrete Mathematics, Advances in Applied Clifford Algebras, and the Journal of Mathematical Analysis and Applications.

Preliminaries
Reviews on noncommutative determinants
Quaternion row and column determinants
The main quaternion generalized inverses
Quaternion core-EP and composite inverses
Applications of generalized inverses in solving
matrix equations
Generalized inverses in solving restricted QTSME

Erscheinungsdatum	22.07.2025
Verlagsort	San Diego
Sprache	englisch
Maße	191 x 235 mm
Gewicht	1210 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	0-443-34145-1 / 0443341451
ISBN-13	978-0-443-34145-8 / 9780443341458
Zustand	Neuware