Ivan Kyrchei (31 results)

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Paperback. Condition: New. 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.…

Condition: New. Provides a comprehensive study of quaternion generalized inverses and introduces the theory of rowcolumn determinants for quaternion matricesDemonstrates direct methods to compute generalized inverses by their determinantal representations.

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Taschenbuch. Condition: Neu. Neuware - 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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Condition: New. Editor(s): Kyrchei, Ivan. Num Pages: 333 pages. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 262 x 187 x 25. Weight in Grams: 802. . 2015. Hardcover. . . . .

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Paperback. Condition: New. 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.…

Condition: New. KlappentextrnrnThis book presents original studies on the leading edge of linear algebra. Each chapter has been carefully selected in an attempt to present substantial research results across a broad spectrum. The main goal of Chapter One is to .

Hardback. Condition: New. New Book, Direct from Publisher.

Condition: New. Editor(s): Kyrchei, Ivan. Num Pages: 333 pages. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 262 x 187 x 25. Weight in Grams: 802. . 2015. Hardcover. . . . . Books ship from the US and Ireland.

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Buch. Condition: Neu. Neuware - This book presents original studies on the leading edge of linear algebra. Each chapter has been carefully selected in an attempt to present substantial research results across a broad spectrum. The main goal of Chapter One is to define and investigate the restricted generalized inverses corresponding to minimization of constrained quadratic form. As stated in Chapter Two, in systems and control theory, Linear Time Invariant (LTI) descriptor (Differential-Algebraic) systems are intimately related to the matrix pencil theory. A review of the most interesting properties of the Projective Equivalence and the Extended Hermite Equivalence classes is presented in the chapter. New determinantal representations of generalized inverse matrices based on their limit representations are introduced in Chapter Three. Using the obtained analogues of the adjoint matrix, Cramer's rules for the least squares solution with the minimum norm and for the Drazin inverse solution of singular linear systems have been obtained in the chapter. In Chapter Four, a very interesting application of linear algebra of commutative rings to systems theory, is explored. Chapter Five gives a comprehensive investigation to behaviors of a general Hermitian quadratic matrix-valued function by using ranks and inertias of matrices. In Chapter Six, the theory of triangular matrices (tables) is introduced. The main 'characters' of the chapter are special triangular tables (which will be called triangular matrices) and their functions paradeterminants and parapermanents. The aim of Chapter Seven is to present the latest developments in iterative methods for solving linear matrix equations. The problems of existence of common eigenvectors and simultaneous triangularization of a pair of matrices over a principal ideal domain with quadratic minimal polynomials are investigated in Chapter Eight. Two approaches to define a noncommutative determinant (a determinant of a matrix with noncommutative elements) are considered in Chapter Nine. The last, Chapter 10, is an example of how the methods of linear algebra are used in natural sciences, particularly in chemistry. In this chapter, it is shown that in a First Order Chemical Kinetics Mechanisms matrix, all columns add to zero, all the diagonal elements are non-positive and all the other matrix entries are non-negative. As a result of this particular structure, the Gershgorin Circles Theorem can be applied to show that all the eigenvalues are negative or zero.…

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Buch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Inverse Problems - Recent Advances and Applications examines some recent advances in inverse problems, new aspects of their mathematical modeling of inverse problems regarding in relation to their applications in physical systems and used the computational methods used. It consists of five chapters divided into two sections. Section 1, 'Modeling and Formulations of Inverse Problems', discusses new approaches to modeling and formulations of inverse problems in some physical systems. Section 2, 'Some Computational Aspects', contains research related to mathematical methods of solving some inverse problems.…

Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Inverse Problems - Recent Advances and Applications examines some recent advances in inverse problems, new aspects of their mathematical modeling of inverse problems regarding in relation to their applications in physical systems and used the computational methods used. It consists of five chapters divided into two sections. Section 1, 'Modeling and Formulations of Inverse Problems', discusses new approaches to modeling and formulations of inverse problems in some physical systems. Section 2, 'Some Computational Aspects', contains research related to mathematical methods of solving some inverse problems.IN TECH d.o.o., Prolaz Marije Krucifikse Kozulic 3, 51000 Rijeka 98 pp. Englisch.…

Paperback. Condition: new. Paperback. Quaternionic Generalized Inverses: Foundations, Theory, Problems, and Solutions This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.