Linear Algebra Ii

Author : Frederick P. Greenleaf,Sophie Marques
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 52,7 Mb
Release : 2020-05-06
Category : Education
ISBN : 9781470454258

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Linear Algebra II by Frederick P. Greenleaf,Sophie Marques Pdf

This book is the second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute. The first three chapters of this second volume round out the coverage of traditional linear algebra topics: generalized eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two chapters are different, being more or less self-contained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important. The book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved.

Author : Anonim
Publisher : Bookboon
Page : 208 pages
File Size : 51,6 Mb
Release : 2024-05-10
Category : Electronic
ISBN : 9788740302417

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Linear Algebra II by Anonim Pdf

Author : Stephan Ramon Garcia,Roger A. Horn
Publisher : Cambridge University Press
Page : 447 pages
File Size : 42,5 Mb
Release : 2017-05-11
Category : Mathematics
ISBN : 9781107103818

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A Second Course in Linear Algebra by Stephan Ramon Garcia,Roger A. Horn Pdf

A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.

Author : David B. Damiano,John B. Little
Publisher : Courier Corporation
Page : 466 pages
File Size : 55,5 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780486469089

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A Course in Linear Algebra by David B. Damiano,John B. Little Pdf

"Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an introduction, definitions, and propositions, in addition to multiple examples, lemmas, theorems, corollaries, andproofs. Each chapter features numerous supplemental exercises, and solutions to selected problems appear at the end. 1988 edition"--

Author : Alexey L. Gorodentsev
Publisher : Springer
Page : 370 pages
File Size : 52,7 Mb
Release : 2017-02-12
Category : Mathematics
ISBN : 9783319508535

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Algebra II by Alexey L. Gorodentsev Pdf

This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.

Author : Edgar G Goodaire
Publisher : World Scientific Publishing Company
Page : 732 pages
File Size : 51,9 Mb
Release : 2013-09-20
Category : Mathematics
ISBN : 9789814508391

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Linear Algebra by Edgar G Goodaire Pdf

This is a matrix-oriented approach to linear algebra that covers the traditional material of the courses generally known as “Linear Algebra I” and “Linear Algebra II” throughout North America, but it also includes more advanced topics such as the pseudoinverse and the singular value decomposition that make it appropriate for a more advanced course as well. As is becoming increasingly the norm, the book begins with the geometry of Euclidean 3-space so that important concepts like linear combination, linear independence and span can be introduced early and in a “real” context. The book reflects the author's background as a pure mathematician — all the major definitions and theorems of basic linear algebra are covered rigorously — but the restriction of vector spaces to Euclidean n-space and linear transformations to matrices, for the most part, and the continual emphasis on the system Ax=b, make the book less abstract and more attractive to the students of today than some others. As the subtitle suggests, however, applications play an important role too. Coding theory and least squares are recurring themes. Other applications include electric circuits, Markov chains, quadratic forms and conic sections, facial recognition and computer graphics.

Author : KAZUO. SUGIHARA MUROTA (MASAAKI.),Masaaki Sugihara
Publisher : Co-Published with World Scientific
Page : 0 pages
File Size : 42,7 Mb
Release : 2022-08-22
Category : Mathematics
ISBN : 9811257051

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Linear Algebra II: Advanced Topics for Applications by KAZUO. SUGIHARA MUROTA (MASAAKI.),Masaaki Sugihara Pdf

This is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course.The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory.The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.

Author : Frederick P. Greenleaf,Sophie Marques
Publisher : American Mathematical Soc.
Page : 261 pages
File Size : 53,7 Mb
Release : 2019-01-30
Category : Algebras, Linear
ISBN : 9781470448714

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Linear Algebra I by Frederick P. Greenleaf,Sophie Marques Pdf

This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise. This first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.

Author : Anonim
Publisher : Unknown
Page : 58 pages
File Size : 43,7 Mb
Release : 1980
Category : Algebras, Linear
ISBN : 0335057969

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Matrices by Anonim Pdf

Author : N. Jacobson
Publisher : Springer
Page : 304 pages
File Size : 48,7 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:49015002165802

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Lectures in Abstract Algebra by N. Jacobson Pdf

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.

Author : Kenneth Kuttler,Ilijas Farah
Publisher : Unknown
Page : 586 pages
File Size : 49,6 Mb
Release : 2020
Category : Algebras, Linear
ISBN : OCLC:1252786692

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A First Course in Linear Algebra by Kenneth Kuttler,Ilijas Farah Pdf

"A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.

Author : A. G. Hamilton
Publisher : Cambridge University Press
Page : 344 pages
File Size : 42,9 Mb
Release : 1989
Category : Mathematics
ISBN : 0521310423

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Linear Algebra: Volume 2 by A. G. Hamilton Pdf

Emphasis is placed on applications in preference to more theoretical aspects throughout this readable introduction to linear algebra for specialists as well as non-specialists. An expanded version of A First Course in Linear Algebra.

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
Page : 387 pages
File Size : 44,6 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780470538166

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Linear Algebra For Dummies by Mary Jane Sterling Pdf

Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants

Author : Open University. Linear Mathematics Course Team
Publisher : Unknown
Page : 52 pages
File Size : 44,7 Mb
Release : 1972
Category : Approximation theory
ISBN : PSU:000029909841

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Least-squares Approximation by Open University. Linear Mathematics Course Team Pdf

Author : Ramji Lal
Publisher : Springer
Page : 432 pages
File Size : 42,7 Mb
Release : 2017-05-03
Category : Mathematics
ISBN : 9789811042560

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Algebra 2 by Ramji Lal Pdf

This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1–5) does not require any background material from Algebra 1, except an understanding of set theory. Linear algebra is the most applicable branch of mathematics, and it is essential for students of science and engineering As such, the text can be used for one-semester courses for these students. The remaining part of the volume discusses Jordan and rational forms, general linear algebra (linear algebra over rings), Galois theory, representation theory (linear algebra over group algebras), and the theory of extension of groups follow linear algebra, and is suitable as a text for the second and third year students specializing in mathematics.