Quaternion Generalized Inverses: Foundations, Theory, Problems, and Solutions - Brossura

Kyrchei

Brossura

ISBN 10: 0443341451 ISBN 13: 9780443341458

Casa editrice: Academic Press, 2025

Riassunto

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.

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Informazioni sull'autore

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.

Dalla quarta di copertina

Quaternionic Generalized Inverses introduces and applies the theory of row-column determinants for the study of quaternion matrices, and thus empowers student and faculty research across wider areas of matrix theory, real, and complex analysis. Here, quaternion linear algebra is considered alongside core aspects of matrix theory, including the construction of an inverse matrix and Cramer's rule for constructing quaternion systems of linear equations, the core inverse, the core-EP inverse, and various composite inverses. Similarly, main frameworks of generalized inverse theory, such as the Moore-Penrose and Drazin inverse, are introduced and demonstrated across exercises in text. Inter-related concepts of differential equations, discrete analogies, advanced calculus modeling, and approximation theory highlight wider areas of applications. Problems, solutions, and chapter conclusions across the book further reinforce learning and application, and recommendations for course integration help faculty incorporate chapter material in their teaching.

Dettagli dell'edizione

• Editore: Academic Press
• Data di pubblicazione: 2025
• Lingua: Inglese
• ISBN 10: 0443341451
• ISBN 13: 9780443341458
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 592
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile