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.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. Biography - p. xvii 8. Preface - p. xix 9. Chapter 1: Preliminaries - p. 1 10. Chapter 2: Reviews on noncommutative determinants - p. 33 11. Chapter 3: Quaternion row and column determinants - p. 51 12. Chapter 4: The main quaternion generalized inverses - p. 107 13. Chapter 5: Quaternion core-EP and composite inverses - p. 207 14. Chapter 6: Applications of generalized inverses in solving matrix equations - p. 277 15. Chapter 7: Generalized inverses in solving restricted QTSME - p. 417 16. Bibliography - p. 549 17. Index - p. 563
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.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. Biography - p. xvii 8. Preface - p. xix 9. Chapter 1: Preliminaries - p. 1 10. Chapter 2: Reviews on noncommutative determinants - p. 33 11. Chapter 3: Quaternion row and column determinants - p. 51 12. Chapter 4: The main quaternion generalized inverses - p. 107 13. Chapter 5: Quaternion core-EP and composite inverses - p. 207 14. Chapter 6: Applications of generalized inverses in solving matrix equations - p. 277 15. Chapter 7: Generalized inverses in solving restricted QTSME - p. 417 16. Bibliography - p. 549 17. Index - p. 563
