Linear Algebra Done Right

Autor: Sheldon Axler
Publisher: Springer
ISBN: 3319110802
File Size: 18,40 MB
Format: PDF, Kindle
Read: 4236
Download or Read Book
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

Linear Algebra Done Right

Autor: Sheldon Axler
Publisher: Springer Science & Business Media
ISBN: 9780387982595
File Size: 69,62 MB
Format: PDF, Docs
Read: 4595
Download or Read Book
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 Done Right

Autor: Sheldon Axler
Publisher: Springer
ISBN: 0387225951
File Size: 75,26 MB
Format: PDF, ePub, Mobi
Read: 6034
Download or Read Book
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

Autor: Klaus Jänich
Publisher: Springer Science & Business Media
ISBN: 9780387941288
File Size: 34,72 MB
Format: PDF, Docs
Read: 9249
Download or Read Book
The original version of this book, handed out to my students in weekly in stallments, had a certain rugged charm. Now that it is dressed up as a Springer UTM volume, I feel very much like Alfred Dolittle at Eliza's wedding. I hope the reader will still sense the presence of a young lecturer, enthusiastically urging his audience to enjoy linear algebra. The book is structured in various ways. For example, you will find a test in each chapter; you may consider the material up to the test as basic and the material following the test as supplemental. In principle, it should be possible to go from the test directly to the basic material of the next chapter. Since I had a mixed audience of mathematics and physics students, I tried to give each group some special attention, which in the book results in certain sections being marked· "for physicists" or "for mathematicians. " Another structural feature of the text is its division into laconic main text, put in boxes, and more talkative unboxed side text. If you follow just the main text, jumping from box to box, you will find that it makes coherent reading, a real "book within the book," presenting all that I want to teach.

Linear Algebra

Autor: Peter Petersen
Publisher: Springer Science & Business Media
ISBN: 1461436125
File Size: 18,27 MB
Format: PDF, ePub
Read: 2000
Download or Read Book
This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distinguishing features that set it apart from other linear algebra texts. For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader. Another motivating aspect of the book is the excellent and engaging exercises that abound in this text. This textbook is written for an upper-division undergraduate course on Linear Algebra. The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text.

Finite Dimensional Vector Spaces

Autor: Paul R. Halmos
Publisher: Courier Dover Publications
ISBN: 0486822265
File Size: 55,72 MB
Format: PDF, Mobi
Read: 3591
Download or Read Book
Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.

Advanced Linear Algebra

Autor: Steven Roman
Publisher: Springer Science & Business Media
ISBN: 9780387274744
File Size: 26,48 MB
Format: PDF, ePub, Docs
Read: 9206
Download or Read Book
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

Calculus With Applications

Autor: Peter D. Lax
Publisher: Springer Science & Business Media
ISBN: 1461479460
File Size: 21,13 MB
Format: PDF, Mobi
Read: 3115
Download or Read Book
Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.

Linear Algebra

Autor: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780817637316
File Size: 53,86 MB
Format: PDF, ePub, Docs
Read: 5262
Download or Read Book
* Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject

Linear Algebra Problem Book

Autor: Paul R. Halmos
Publisher: MAA
ISBN: 9780883853221
File Size: 67,84 MB
Format: PDF, ePub, Mobi
Read: 9690
Download or Read Book
Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions.