The Mathematics Of Matrices
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The Mathematics Of Matrices
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Author : Philip J. Davis
language : en
Publisher:
Release Date : 1984
The Mathematics Of Matrices written by Philip J. Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Matrices And Linear Algebra
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Author : Hans Schneider
language : en
Publisher: Courier Corporation
Release Date : 1989-01-01
Matrices And Linear Algebra written by Hans Schneider and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it. This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations. Table of Contents: l. The Algebra of Matrices 2. Linear Equations 3. Vector Spaces 4. Determinants 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Inner Product Spaces 8. Applications to Differential Equations For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.
Matrices And Transformations
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Author : Anthony J. Pettofrezzo
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Matrices And Transformations written by Anthony J. Pettofrezzo and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.
The Theory Of Matrices
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Author : Peter Lancaster
language : en
Publisher: Academic Press
Release Date : 1985-05-28
The Theory Of Matrices written by Peter Lancaster and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-05-28 with Computers categories.
Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.
The Theory Of Matrices
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Author : Cyrus Colton MacDuffee
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Theory Of Matrices written by Cyrus Colton MacDuffee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Matric algebra is a mathematical abstraction underlying many seemingly diverse theories. Thus bilinear and quadratic forms, linear associative algebra (hypercomplex systems), linear homogeneous trans formations and linear vector functions are various manifestations of matric algebra. Other branches of mathematics as number theory, differential and integral equations, continued fractions, projective geometry etc. make use of certain portions of this subject. Indeed, many of the fundamental properties of matrices were first discovered in the notation of a particular application, and not until much later re cognized in their generality. It was not possible within the scope of this book to give a completely detailed account of matric theory, nor is it intended to make it an authoritative history of the subject. It has been the desire of the writer to point out the various directions in which the theory leads so that the reader may in a general way see its extent. While some attempt has been made to unify certain parts of the theory, in general the material has been taken as it was found in the literature, the topics discussed in detail being those in which extensive research has taken place. For most of the important theorems a brief and elegant proof has sooner or later been found. It is hoped that most of these have been incorporated in the text, and that the reader will derive as much plea sure from reading them as did the writer.
Nonnegative Matrices In The Mathematical Sciences
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Author : Abraham Berman
language : en
Publisher: SIAM
Release Date : 1994-01-01
Nonnegative Matrices In The Mathematical Sciences written by Abraham Berman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993. Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices. On the way, semigroups of nonnegative matrices and symmetric nonnegative matrices are discussed. Later, applications of nonnegativity and M-matrices are given; for numerical analysis the example is convergence theory of iterative methods, for probability and statistics the examples are finite Markov chains and queuing network models, for mathematical economics the example is input-output models, and for mathematical programming the example is the linear complementarity problem. Nonnegativity constraints arise very naturally throughout the physical world. Engineers, applied mathematicians, and scientists who encounter nonnegativity or generalizations of nonegativity in their work will benefit from topics covered here, connecting them to relevant theory. Researchers in one area, such as queuing theory, may find useful the techniques involving nonnegative matrices used by researchers in another area, say, mathematical programming. Exercises and biographical notes are included with each chapter.
The Mathematical Matrix
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-15
The Mathematical Matrix written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-15 with Mathematics categories.
Embark on a Mathematical Odyssey with The Mathematical Matrix: A Comprehensive Guide to Unraveling the Mysteries of Numbers, Shapes, and Patterns The Mathematical Matrix is an indispensable resource for anyone seeking to deepen their understanding of mathematics, from students and teachers to enthusiasts and professionals. This comprehensive guide takes you on a captivating journey through the world of numbers, shapes, and patterns, providing clear explanations, illustrative examples, and thought-provoking exercises to reinforce understanding. Divided into ten chapters, The Mathematical Matrix covers a wide range of mathematical topics, from the fundamentals of arithmetic and algebra to the complexities of calculus and statistics. Each chapter delves into a specific mathematical concept, exploring its intricacies and applications in a clear and engaging manner. One of the unique features of The Mathematical Matrix is its emphasis on the connections between mathematics and other disciplines. Throughout the book, you will discover how mathematics is used in fields as diverse as art, music, computer science, and finance. These connections highlight the versatility and applicability of mathematics, demonstrating its power to solve real-world problems and enhance our understanding of the world around us. The Mathematical Matrix also emphasizes the importance of mathematical thinking and problem-solving skills. You will learn how to approach mathematical problems systematically, break them down into smaller steps, and apply appropriate mathematical techniques to find solutions. These skills are essential not only for success in mathematics but also for success in many other areas of life. As you journey through the chapters of The Mathematical Matrix, you will encounter some of the greatest minds in mathematics, from ancient mathematicians like Euclid and Archimedes to modern mathematicians like Alan Turing and Srinivasa Ramanujan. Their stories and contributions to the field of mathematics provide inspiration and motivation for us to continue exploring the depths of this fascinating subject. Whether you are a seasoned mathematician or just beginning your mathematical journey, The Mathematical Matrix is your guide to unlocking the secrets of the universe through the power of mathematics. Open its pages and embark on a journey of discovery that will change the way you see the world. If you like this book, write a review!
Nonnegative Matrices In The Mathematical Sciences
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Author : Abraham Berman
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Nonnegative Matrices In The Mathematical Sciences written by Abraham Berman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
Matrix Mathematics
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Author : Dennis S. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 2009-07-06
Matrix Mathematics written by Dennis S. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-06 with Mathematics categories.
When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing
The Mathematics Of Harmony
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Author : Alexey Stakhov
language : en
Publisher: World Scientific
Release Date : 2009
The Mathematics Of Harmony written by Alexey Stakhov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."