Linear Algebra And Matrices Topics For A Second Course

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Linear Algebra and Matrices: Topics for a Second Course

Helene Shapiro
Linear Algebra and Matrices Topics for a Second Course Book PDF

Author : Helene Shapiro
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 50,7 Mb
Release : 2015-10-08
Category : Mathematics
ISBN : 9781470418526

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Linear Algebra and Matrices: Topics for a Second Course by Helene Shapiro Pdf

Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.

A Second Course in Linear Algebra

Stephan Ramon Garcia,Roger A. Horn
A Second Course in Linear Algebra Book PDF

Author : Stephan Ramon Garcia,Roger A. Horn
Publisher : Cambridge University Press
Page : 447 pages
File Size : 50,6 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.

A Second Course in Linear Algebra

William Clough Brown
A Second Course in Linear Algebra Book PDF

Author : William Clough Brown
Publisher : Wiley-Interscience
Page : 298 pages
File Size : 51,8 Mb
Release : 1988
Category : Mathematics
ISBN : UVA:X001401506

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A Second Course in Linear Algebra by William Clough Brown Pdf

This textbook for senior undergraduate and first year graduate-level courses in linear algebra and analysis, covers linear algebra, multilinear algebra, canonical forms of matrices, normal linear vector spaces and inner product spaces. These topics provide all of the prerequisites for graduate students in mathematics to prepare for advanced-level work in such areas as algebra, analysis, topology and applied mathematics.

Matrix Theory: A Second Course

James M. Ortega
Matrix Theory A Second Course Book PDF

Author : James M. Ortega
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 51,7 Mb
Release : 1987-02-28
Category : Mathematics
ISBN : 0306424339

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Matrix Theory: A Second Course by James M. Ortega Pdf

Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.

Matrix Theory: A Second Course

James M. Ortega
Matrix Theory A Second Course Book PDF

Author : James M. Ortega
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 40,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489904713

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Matrix Theory: A Second Course by James M. Ortega Pdf

Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.

Linear Algebra: Core Topics For The Second Course

Dragu Atanasiu,Piotr Mikusinski
Linear Algebra Core Topics For The Second Course Book PDF

Author : Dragu Atanasiu,Piotr Mikusinski
Publisher : World Scientific
Page : 333 pages
File Size : 53,7 Mb
Release : 2023-01-04
Category : Mathematics
ISBN : 9789811258565

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Linear Algebra: Core Topics For The Second Course by Dragu Atanasiu,Piotr Mikusinski Pdf

This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.

Linear Algebra

Robert J. Valenza
Linear Algebra Book PDF

Author : Robert J. Valenza
Publisher : Springer
Page : 237 pages
File Size : 40,6 Mb
Release : 1999-02-01
Category : Mathematics
ISBN : 9780387940991

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Linear Algebra by Robert J. Valenza Pdf

Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.

Introduction to Linear and Matrix Algebra

Nathaniel Johnston
Introduction to Linear and Matrix Algebra Book PDF

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 43,9 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119

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Introduction to Linear and Matrix Algebra by Nathaniel Johnston Pdf

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.

Matrix Mathematics

Stephan Ramon Garcia,Roger A. Horn
Matrix Mathematics Book PDF

Author : Stephan Ramon Garcia,Roger A. Horn
Publisher : Cambridge University Press
Page : 492 pages
File Size : 43,9 Mb
Release : 2023-05-25
Category : Mathematics
ISBN : 9781108945592

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Matrix Mathematics by Stephan Ramon Garcia,Roger A. Horn Pdf

Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.

Linear Algebra Done Right

Sheldon Axler
Linear Algebra Done Right Book PDF

Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 52,8 Mb
Release : 1997-07-18
Category : Mathematics
ISBN : 0387982590

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Linear Algebra Done Right by Sheldon Axler Pdf

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: Core Topics For The First Course

Dragu Atanasiu,Piotr Mikusinski
Linear Algebra Core Topics For The First Course Book PDF

Author : Dragu Atanasiu,Piotr Mikusinski
Publisher : World Scientific
Page : 465 pages
File Size : 51,8 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9789811215049

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Linear Algebra: Core Topics For The First Course by Dragu Atanasiu,Piotr Mikusinski Pdf

The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space ℝn, orthogonality in ℝn, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices.In the first nine chapters everything is formulated in terms of ℝn. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises.

The Foundations of Mathematics

Kenneth Kunen
The Foundations of Mathematics Book PDF

Author : Kenneth Kunen
Publisher : Unknown
Page : 251 pages
File Size : 43,6 Mb
Release : 2009
Category : Mathematics
ISBN : 1904987141

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The Foundations of Mathematics by Kenneth Kunen Pdf

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Coding the Matrix

Philip N. Klein
Coding the Matrix Book PDF

Author : Philip N. Klein
Publisher : Unknown
Page : 530 pages
File Size : 42,8 Mb
Release : 2013-07
Category : Algebras, Linear
ISBN : 061585673X

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Coding the Matrix by Philip N. Klein Pdf

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.

Linear Algebra

Kuldeep Singh
Linear Algebra Book PDF

Author : Kuldeep Singh
Publisher : Oxford University Press
Page : 617 pages
File Size : 44,5 Mb
Release : 2013-10
Category : Mathematics
ISBN : 9780199654444

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Linear Algebra by Kuldeep Singh Pdf

"This book is intended for first- and second-year undergraduates arriving with average mathematics grades ... The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to all of the set problems freely available online http://www.oup.co.uk/companion/singh" -- From preface.

Matrices and Linear Algebra

Hans Schneider,George Phillip Barker
Matrices and Linear Algebra Book PDF

Author : Hans Schneider,George Phillip Barker
Publisher : Courier Corporation
Page : 430 pages
File Size : 49,8 Mb
Release : 2012-06-08
Category : Mathematics
ISBN : 9780486139302

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Matrices and Linear Algebra by Hans Schneider,George Phillip Barker Pdf

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.