Ivan I. Kyrchei

Quaternion Generalized Inverses (eBook, ePUB)

Foundations, Theory, Problems, and Solutions

• Format: ePub

Produktbeschreibung

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.. Introduces and applies linear algebra and matrix theory for the study of real and complex number fields. Demonstrates direct methods to compute generalized inverses by their representations. Features sections on practical applications and ongoing research. Includes problems, solutions, and chapter core concept reviews, as well as recommendations for course integration

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Produktdetails

• Verlag: Elsevier Science & Techn.
• Seitenzahl: 500
• Erscheinungstermin: 2. März 2026
• Englisch
• ISBN-13: 9780443341465
• Artikelnr.: 74861402

Autorenporträt

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.

Inhaltsangabe

1. Preliminaries
2. Reviews on noncommutative determinants
3. Quaternion row and column determinants
4. The main quaternion generalized inverses
5. Quaternion core-EP and composite inverses
6. Applications of generalized inverses in solving
7. matrix equations
8. Generalized inverses in solving restricted QTSME