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This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications. 

20 Lectures on Eigenvectors Eigenvalues and Their Applications Problems in Chemical Engineering

This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications. 

20 Lectures on Eigenvectors Eigenvalues and Their Applications Problems in Chemical Engineering

This book covers linear algebra methods for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions. Financial Applications · The Arrow—Debreu one period market model · One period index options arbitrage · Covariance and correlation matrix estimation from time series data · Ordinary least squares for implied volatility computation · Minimum variance portfolios and maximum return portfolios · Value at Risk and portfolio VaR Linear Algebra Topics · LU and Cholesky decompositions and linear solvers · Optimal solvers for tridiagonal symmetric positive matrices · Ordinary least squares and linear regression · Linear Transformation Property · Efficient cubic spline interpolation · Multivariate normal random variables The book is written in a similar spirit as the best selling ``A Primer for the Mathematics of Financial Engineering" by the same author, and should accordingly be useful to a similarly large audience: · Prospective students for financial engineering or mathematical finance programs will be able to self-study material that will prove very important in their future studies · Finance practitioners will find mathematical underpinnings for many methods used in practice, furthering the ability to expand upon these methods · Academics teaching financial engineering courses will be able to use this book as textbook, or as reference book for numerical linear algebra methods with financial applications.

This book covers linear algebra methods for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions. Financial Applications · The Arrow—Debreu one period market model · One period index options arbitrage · Covariance and correlation matrix estimation from time series data · Ordinary least squares for implied volatility computation · Minimum variance portfolios and maximum return portfolios · Value at Risk and portfolio VaR Linear Algebra Topics · LU and Cholesky decompositions and linear solvers · Optimal solvers for tridiagonal symmetric positive matrices · Ordinary least squares and linear regression · Linear Transformation Property · Efficient cubic spline interpolation · Multivariate normal random variables The book is written in a similar spirit as the best selling ``A Primer for the Mathematics of Financial Engineering" by the same author, and should accordingly be useful to a similarly large audience: · Prospective students for financial engineering or mathematical finance programs will be able to self-study material that will prove very important in their future studies · Finance practitioners will find mathematical underpinnings for many methods used in practice, furthering the ability to expand upon these methods · Academics teaching financial engineering courses will be able to use this book as textbook, or as reference book for numerical linear algebra methods with financial applications.

This book represents the first treatment of computable analysis at the graduate level within the tradition of classical mathematical reasoning. Among the topics dealt with are: classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The book is self-contained, and yet sufficiently detailed to provide an introduction to research in this area.

Intended for a serious first course or a second course in linear algebra, this book carries students beyond eigenvalues and eigenvectors to the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices. The authors present the material from a structural point of view: fundamental algebraic properties of the entities involved are emphasized. The approach is particularly important because the mathematical systems encountered in linear algebra furnish a wealth of examples for the structures studied in more advanced courses. By taking a straight and smooth path to the heart of linear algebra, students will be able to make the transition from the intuitive developments of courses at a lower level to the more abstract treatments encountered later.

This text covers a standard first course: Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some brief topics, such as applications.What sets it apart is careful motivation, many examples, and extensive exercise sets. Together, these help each student master the material of the course and also help an instructor develop that student's level of mathematical maturity.

Matrices and Linear System of Equations. 2. Eigenvalues, Eigenvectors and Quadratic Forms. 3. Multiple Integrals. 4. Special Function. 5. Vector Differentiation. 6. Vector Integration. 7. Curve Tracing. 8. Some Applications of Multiple Integrals. Index. This comprehensive and self-contained text provides a thorough understanding of the concepts and applications of Linear algebra and Vector Calculus. It is written in such a manner that beginners can develop an interest in the subject. Besides providing the essentials of the theory, the book helps in developing problem-solving techniques and sharpens the skill of logical thinking. The book covers a wide range of topics such as Matrices, vector Algebra, Vector calculus, Multiple Integrals, Applications of differential equations. It too serves as a textbook for the students of under graduation, post-graduation and Engineering. Each chapter has been planned as an independent unit. The exercise questions given at the end of each chapter are also useful for the competitive examinations like GATE, IES, ICS. Key Features Each chapter is saturated with much needed texts, and suitable illustrations. The language is simple and precise. Complete proofs/verifications provided wherever necessary. Exercises with hints and answers are given at the end of each chapter. (jacket)

This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.

This book covers the material of an introductory course in linear algebra. Topics include sets and maps, vector spaces, bases, linear maps, matrices, determinants, systems of linear equations, Euclidean spaces, eigenvalues and eigenvectors, diagonalization of self-adjoint operators, and classification of matrices. It contains multiple choice tests with commented answers.

This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.

After transitioning from solving systems of two linear equations to solving general systems, this textbook introduces the algebraic properties of matrix operations, determinants, vector spaces, eigenvalues, eigenvectors, linear transformations, inner product spaces, numerical techniques, and linear programming. The fifth edition adds sections on matrix multiplication in terms of columns, and orthogonal transformations. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications. Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices and their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra. Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.

This introduction to linear algebra offers a balance between abstraction/theory and computational skills. KEY TOPICS: Linear Equations and Matrices. Real Vector Spaces. Inner Product Spaces. Linear Transformations and Matrices. Determinants. Eigenvalues and Eigenvectors. Differential Equations. MATLAB for Linear Algebra. MATLAB Exercises. For anyone needing a basic understanding of matrix theory or computational skills involving linear algebra.

Linear Algebra provides a valuable introduction to the basic theory of matrices and vector spaces. The book covers: matrices, vector spaces, bases, and dimension; inner products, bilinear and sesquilinear forms over vector spaces; linear transformations, eigenvalues and eigenvectors, diagonalization, and Jordan normal form; and fields and polynomials over fields. Abstract methods are illustrated with concrete examples, and more detailed examples highlight applications of linear algebra to analysis, geometry, differential equations, relativity and quantum mechanics. Rigorous without being unnecessarily abstract, this useful and concise guide to the subject will be important reading for all students in mathematics and related fields.

A thorough first course in linear algebra, this two-part treatment begins with the basic theory of vector spaces and linear maps, including dimension, determinants, eigenvalues, and eigenvectors. The second section addresses more advanced topics such as the study of canonical forms for matrices. The treatment can be tailored to satisfy the requirements of both introductory and advanced courses. Introductory courses that also serve as an initiation into formal mathematics will focus on the first six chapters. Students already schooled in matrices and linear mappings as well as theorem-proving will quickly proceed to selected chapters from part two. The selection can emphasize algebra or analysis/geometry, as needed. Ample examples, applications, and exercises appear throughout the text, which is supplemented by three helpful Appendixes.

This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.

Intended for a serious first course or a second course in linear algebra, this book carries students beyond eigenvalues and eigenvectors to the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices. The authors present the material from a structural point of view: fundamental algebraic properties of the entities involved are emphasized. The approach is particularly important because the mathematical systems encountered in linear algebra furnish a wealth of examples for the structures studied in more advanced courses. By taking a straight and smooth path to the heart of linear algebra, students will be able to make the transition from the intuitive developments of courses at a lower level to the more abstract treatments encountered later.