Kyrchei ivan (18 Ergebnisse)
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Zustand: 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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Einband - fest (Hardcover). Zustand: New.
Quaternion Generalized Inverses : Foundations, Theory, Problems, and Solutions
Ivan I. (Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS Kyrchei
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Taschenbuch. Zustand: 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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Zustand: 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 .
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Buch. Zustand: Neu. Neuware - Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. Systems of linear equations with several unknowns are naturally represented using the formalism of matrices and vectors. So we arrive at the matrix algebra, etc. Linear algebra is central to… almost all areas of mathematics. Many ideas and methods of linear algebra were generalised to abstract algebra. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Linear algebra is also used in most sciences and engineering areas because it allows for the modelling of many natural phenomena, and efficiently computes with such models. ''Hot Topics in Linear Algebra'' presents original studies in some areas of the leading edge of linear algebra. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed herein include recent advances in analysis of various dynamical systems based on the Gradient Neural Network; Cramer's rules for quaternion generalized Sylvester-type matrix equations by using noncommutative row-column determinants; matrix algorithms for finding the generalized bisymmetric solution pair of general coupled Sylvester-type matrix equations; explicit solution formulas of some systems of mixed generalised Sylvester-type quaternion matrix equations; new approaches to studying the properties of Hessenberg matrices by using triangular tables and their functions; researching of polynomial matrices over a field with respect to semi-scalar equivalence; mathematical modelling problems in chemistry with applying mixing problems, which the associated MP-matrices; and some visual apps, designed in Scilab, for the learning of different topics of linear algebra.
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Zustand: 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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EUR 258,64
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Buch. Zustand: 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 correspondi…ng 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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Zustand: Used: Like New. LIVRE A L?ETAT DE NEUF. EXPEDIE SOUS 3 JOURS OUVRES. NUMERO DE SUIVI COMMUNIQUE AVANT ENVOI, EMBALLAGE RENFORCE. EAN:9781536177701.
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Zustand: Used: Like New. LIVRE A L?ETAT DE NEUF. EXPEDIE SOUS 3 JOURS OUVRES. NUMERO DE SUIVI COMMUNIQUE AVANT ENVOI, EMBALLAGE RENFORCE. EAN:9781685073565.
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Zustand: Used: Like New. LIVRE A L?ETAT DE NEUF. EXPEDIE SOUS 3 JOURS OUVRES. NUMERO DE SUIVI COMMUNIQUE AVANT ENVOI, EMBALLAGE RENFORCE. EAN:9781634635653.
