Introduction to Modern Algebra and Matrix Theory: Second Edition

Overview

This unique text provides students with a single-volume treatment of the basics of calculus and analytic geometry. It reflects the teaching methods and philosophy of Otto Schreier, an influential mathematician and professor. The order of its presentation promotes an intuitive approach to calculus, and it offers a strong emphasis on algebra with minimal prerequisites.
Starting with affine space and linear equations, the text proceeds to considerations of Euclidean space and the ...

See more details below
Other sellers (Paperback)
  • All (22) from $6.40   
  • New (16) from $9.39   
  • Used (6) from $6.40   
Introduction to Modern Algebra and Matrix Theory

Available on NOOK devices and apps  
  • NOOK Devices
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK Study
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$13.99
BN.com price
(Save 44%)$24.99 List Price

Overview

This unique text provides students with a single-volume treatment of the basics of calculus and analytic geometry. It reflects the teaching methods and philosophy of Otto Schreier, an influential mathematician and professor. The order of its presentation promotes an intuitive approach to calculus, and it offers a strong emphasis on algebra with minimal prerequisites.
Starting with affine space and linear equations, the text proceeds to considerations of Euclidean space and the theory of determinants, field theory and the fundamental theorem of algebra, elements of group theory, and linear transformations and matrices. Numerous exercises at the end of each section form important supplements to the text.

Read More Show Less

Product Details

  • ISBN-13: 9780486482200
  • Publisher: Dover Publications
  • Publication date: 7/19/2011
  • Series: Dover Books on Mathematics Series
  • Pages: 400
  • Sales rank: 834,820
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.80 (d)

Table of Contents

Editor's Preface iii

Translators' Preface iii

Authors' Preface v

Chapter I Affine Space; Linear Equations

§ 1 n-dimensional Affine Space 1

§ 2 Vectors 6

§ 3 The Concept of Linear Dependence 16

§ 4 Vector Spaces in Rn 19

§ 5 Linear Spaces 27

§ 6 Linear Equations 34

Homogeneous Linear Equations 36

Non-homogeneous Linear Equations 40

Geometric Applications 44

Chapter II Euclidean Space; Theory of Determinants

§ 7 Euclidean Length 50

Appendix to § 7 Calculating with the Summation Sign 60

§ 8 Volumes and Determinants 63

Fundamental Properties of Determinants 69

Existence and Uniqueness of Determinants 74

Volumes 83

§ 9 The Principal Theorems of Determinant Theory 87

The Complete Development of a Determinant 87

The Determinant as a Function of its Column Vectors 89

The Multiplication Theorem 96

The Development of a Determinant by Rows or Columns 98

Determinants and Linear Equations 100

Laplace's Expansion Theorem 105

§ 10 Transformation of Coordinates 117

General Linear Coordinate Systems 117

Cartesian Coordinate Systems 126

Continuous Deformation of a Linear Coordinate System 131

§ 11 Construction of Normal Orthogonal Systems and Applications 140

§ 12 Rigid Motions 153

Rigid Motions in R2 162

Rigid Motions in R3 168

§ 13 Affine Transformations 180

Chapter III Field Theory; The Fundamental Theorem of Algebra

§ 14 The Concept of a Field 187

§ 15 Polynomials over a Field 204

§ 16 The Field of Complex Numbers 218

§ 17 The Fundamental Theorem of Algebra 230

Chapter IV Elements of Group Theory

§ 18 The Concept of a Group 245

§ 19 Subgroups; Examples 251

§ 20 The Basis Theorem for Abelian Groups 260

Chapter V Linear Transformations and Matrices

§ 21 The Algebra of Linear Transformations 273

§ 22 Calculation with Matrices 283

Linear Transformations Under a Change of Coordinate System 293

The Determinant of a Linear Transformations 296

Linear Dependence of Matrices 297

Calculation With Matrix Polynomials 298

The Transpose of a Matrix 301

§ 23 The Minimal Polynomial; Invariant Subspaces 303

The Minimal Polynomial 303

Invariant Subspaces 305

The Nullspace of a Linear Transformation f(σ) 306

Decomposition of L into Invariant Subspaces 310

Geometric Interpretation 315

§ 24 The Diagonal Form and its Applications 320

Unitary Transformations 327

Orthogonal Transformations 334

Hermitian and Symmetric Matrices (Principal Axis Transformations) 340

§ 25 The Elementary Divisors of a Polynomial Matrix 344

§ 26 The Normal Form 355

Consequences 363

Linear Transformation with Prescribed Elementary Divisors 365

The Jordan Normal Form 367

Index 373

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)