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Author: Gerald D. Ling Publisher: ISBN: Category : Mathematics Languages : en Pages : 334
Book Description
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalised in operator theory. It has extensive applications in the natural sciences and the social sciences, since non-linear models can often be approximated by linear ones.
Author: Gerald D. Ling Publisher: ISBN: Category : Mathematics Languages : en Pages : 334
Book Description
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalised in operator theory. It has extensive applications in the natural sciences and the social sciences, since non-linear models can often be approximated by linear ones.
Author: Steven Roman Publisher: Springer Science & Business Media ISBN: 038727474X Category : Mathematics Languages : en Pages : 486
Book Description
Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
Author: Kevin O'Meara Publisher: OUP USA ISBN: 0199793735 Category : Mathematics Languages : en Pages : 423
Book Description
This book develops the Weyr matrix canonical form, a largely unknown cousin of the Jordan form. It explores novel applications, including include matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry. Module theory and algebraic geometry are employed but with self-contained accounts.
Author: Nathaniel Johnston Publisher: Springer Nature ISBN: 3030528111 Category : Mathematics Languages : en Pages : 482
Book Description
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
Author: Ivan Kyrchei Publisher: Nova Science Publishers ISBN: 9781634635653 Category : Algebras, Linear Languages : en Pages : 0
Book Description
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.
Author: Ivan Kyrchei Publisher: ISBN: 9781536177701 Category : Algebras, Linear Languages : en Pages : 307
Book Description
"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 generalized 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 modeling 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 generalized 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 modeling 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"--
Author: Hugo Woerdeman Publisher: CRC Press ISBN: 149875404X Category : Mathematics Languages : en Pages : 348
Book Description
Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author’s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products. Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.
Author: Rajnikant Sinha Publisher: Springer Nature ISBN: 9811398496 Category : Mathematics Languages : en Pages : 351
Book Description
This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
Author: Ferrante Neri Publisher: Springer ISBN: 3030213218 Category : Computers Languages : en Pages : 574
Book Description
This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory. It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who need a theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.
Author: V. Madhu Publisher: Springer ISBN: 3030011208 Category : Mathematics Languages : en Pages : 485
Book Description
This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017 - Volume I. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.
Author: Gerald D. Ling
Author: Gerald D. Ling
Author: Steven Roman
Author: Kevin O'Meara
Author: Nathaniel Johnston
Author: Ivan Kyrchei
Author: Ivan Kyrchei
Author: Hugo Woerdeman
Author: Rajnikant Sinha
Author: Ferrante Neri
Author: V. Madhu