Linear And Matrix Algebra
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Advanced Linear And Matrix Algebra
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Author : Nathaniel Johnston
language : en
Publisher: Springer Nature
Release Date : 2021-05-19
Advanced Linear And Matrix Algebra written by Nathaniel Johnston and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-19 with Mathematics categories.
This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques. Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author’s companion volume, Introduction to Linear and Matrix Algebra.
Introduction To Linear And Matrix Algebra
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Author : Nathaniel Johnston
language : en
Publisher: Springer Nature
Release Date : 2021-05-19
Introduction To Linear And Matrix Algebra written by Nathaniel Johnston and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-19 with Mathematics categories.
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.
Matrices And Linear Algebra
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Author : Hans Schneider
language : en
Publisher: Courier Corporation
Release Date : 2012-06-08
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 2012-06-08 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.
Matrix Algebra
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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06
Matrix Algebra written by James E. Gentle 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 2007-08-06 with Mathematics categories.
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Elementary Linear And Matrix Algebra
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Author : John T. Moore
language : en
Publisher: McGraw-Hill Companies
Release Date : 1972
Elementary Linear And Matrix Algebra written by John T. Moore and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Matrix Algebra For Linear Models
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Author : Marvin H. J. Gruber
language : en
Publisher: John Wiley & Sons
Release Date : 2013-12-31
Matrix Algebra For Linear Models written by Marvin H. J. Gruber and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
Essential Linear Algebra With Applications
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Author : Titu Andreescu
language : en
Publisher: Springer
Release Date : 2014-10-14
Essential Linear Algebra With Applications written by Titu Andreescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Mathematics categories.
Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject’s hallmark.
Linear Algebra With Mathematica
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Author : Fred Szabo
language : en
Publisher: Academic Press
Release Date : 2000-02-14
Linear Algebra With Mathematica written by Fred Szabo and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-14 with Computers categories.
Linear Algebra: An Introduction With Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics. Includes a thematic presentation of linear algebra Provides a systematic integration of Mathematica Encourages students to appreciate the benefits of mathematical rigor All exercises can be solved with Mathematica
Matrices And Linear Algebra With Gap
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Author : Akhilesh Chandra Yadav
language : en
Publisher: Akhilesh Chandra Yadav
Release Date : 2020-08-16
Matrices And Linear Algebra With Gap written by Akhilesh Chandra Yadav and has been published by Akhilesh Chandra Yadav this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-16 with Language Arts & Disciplines categories.
This book covers an undergraduate course on Matrix theory and Linear Algebra. It covers the following main topics: Matrix Algebra, Determinants, Rank of a Matrix, Linear Equations, Eigenvalues and Eigenvectors, Vector spaces, Linear transformations, Dual spaces, Annihilators, Matrix representations of linear transformations, Inner product spaces, Orthogonality and Bilinear and quadratic forms. Application of GAP softwares in Matrices and Linear Algebra is also given. It is useful in several for several degree courses like BBA, BCA, BA-Maths, B.Sc/M.Sc-Maths. This book is also helpful for several competitive exams like NET and GATE.
Linear And Matrix Algebra
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Author : Nathaniel Johnston
language : en
Publisher: Springer
Release Date : 2021-07-02
Linear And Matrix Algebra written by Nathaniel Johnston and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-02 with Mathematics categories.
This textbook set 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 two books. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. The second volume builds on the introductory foundations laid in the first. Linear and Matrix Algebra presents a unified pathway from introductory to advanced techniques. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. To begin, students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. On completing the set, students will be equipped with the advanced tools and concepts needed for further study in mathematics, data analysis, and beyond. Instructors will appreciate the ample opportunities to select topics that align with the needs of each classroom, along with the convenience of consistency across the undergraduate linear algebra curriculum.