Linear Algebra Done Right
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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.
Linear Algebra Problem Book
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Author : Paul R. Halmos
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-12-31
Linear Algebra Problem Book written by Paul R. Halmos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-31 with Mathematics categories.
Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.
Measure Integration Real Analysis
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Author : Sheldon Axler
language : en
Publisher: Springer
Release Date : 2019-12-24
Measure Integration Real Analysis written by Sheldon Axler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Mathematics categories.
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.
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 Via Exterior Products
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Author : Sergei Winitzki
language : en
Publisher: Sergei Winitzki
Release Date : 2009-07-30
Linear Algebra Via Exterior Products written by Sergei Winitzki and has been published by Sergei Winitzki this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Science categories.
This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
Advanced Linear Algebra
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
Advanced Linear Algebra written by Steven Roman 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 2007-12-31 with Mathematics categories.
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
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 : Jim Hefferon
language : en
Publisher: Orthogonal Publishing L3c
Release Date : 2015
Linear Algebra written by Jim Hefferon and has been published by Orthogonal Publishing L3c this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Algebras, Linear categories.
"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 topics such as brief applications. What sets it apart is careful motivation, many examples, and extensive exercise sets. Together these help each student master the material of this course, and also help an instructor develop that student's level of mathematical maturity. This book has been available online for many years and is widely used, both in classrooms and for self-study. It is supported by worked answers for all exercises, beamer slides for classroom use, and a lab manual of computer work"--Page 4 of cover.
Linear Algebra In Action
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Author : Harry Dym
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-31
Linear Algebra In Action written by Harry Dym and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as graduate students. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.