Linear Mathematics
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On The Teaching Of Linear Algebra
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Author : J.-L. Dorier
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-09-30
On The Teaching Of Linear Algebra written by J.-L. Dorier 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 2000-09-30 with Education categories.
This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues.
Linear Algebra
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Author : H. E. Rose
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Linear Algebra written by H. E. Rose 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 2002 with Mathematics categories.
Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach - linear algebra contains some fine pure mathematics. Main topics: - vector spaces and algebras, dimension, linear maps, direct sums, and (briefly) exact sequences - matrices and their connections with linear maps, determinants (properties proved using some elementary group theory), and linear equations - Cayley-Hamilton and Jordan theorems leading to the spectrum of a linear map - this provides a geometric-type description of these maps - Hermitian and inner product spaces introducing some metric properties (distance, perpendicularity etc.) into the theory, also unitary and orthogonal maps and matrices - applications to finite fields, mathematical coding theory, finite matrix groups, the geometry of quadratic forms, quaternions and Cayley numbers, and some basic group representation theory A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. Some of these are theoretical and some numerical, both types are important. No particular computer algebra package is discussed but a number of the exercises are intended to be solved using one of these packages chosen by the reader.The approach is pure-mathematical, and the intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students.
Linear Algebra
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Author : Georgi? Evgen?evich Shilov
language : en
Publisher: Courier Corporation
Release Date : 1977-06-01
Linear Algebra written by Georgi? Evgen?evich Shilov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-06-01 with Mathematics categories.
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Linear Algebra
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Author : Jörg Liesen
language : en
Publisher: Springer
Release Date : 2015-11-20
Linear Algebra written by Jörg Liesen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-20 with Mathematics categories.
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
Linear Algebra Done Right
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Author : Sheldon Axler
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-18
Linear Algebra Done Right written by Sheldon Axler 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 1997-07-18 with Mathematics categories.
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
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.
Introduction To Linear Algebra
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Author : Gilbert Strang
language : en
Publisher: Wellesley College
Release Date : 1993
Introduction To Linear Algebra written by Gilbert Strang and has been published by Wellesley College this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.
Introduction To Applied Linear Algebra
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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07
Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Linear Algebra And Matrix Theory
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Author : Robert R. Stoll
language : en
Publisher: Courier Corporation
Release Date : 2012-10-17
Linear Algebra And Matrix Theory written by Robert R. Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-17 with Mathematics categories.
Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.
Linear Algebra Through Geometry
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Author : Thomas Banchoff
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-09-10
Linear Algebra Through Geometry written by Thomas Banchoff 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 1993-09-10 with Mathematics categories.
This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.