Linear Algebra

Linear Algebra : A First Course with Applications

  • Electronic book text
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Description

Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, this classroom-tested book gives students enough time to absorb the material by focusing on vector spaces early on and using computational sections as numerical interludes. It offers introductions to Maple (TM), MATLAB (R), and TI-83 Plus for calculating matrix inverses, determinants, eigenvalues, and eigenvectors. Moving from the specific to the general, the author raises questions, provides motivation, and discusses strategy before presenting answers. Discussions of motivation and strategy include content and context to help students learn.show more

Product details

  • Electronic book text | 752 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 1000 equations; 15 Tables, black and white; 116 Illustrations, black and white
  • 1584887834
  • 9781584887836

Table of contents

Preface for the Instructor Foreword A Little Logic Logical Foundations Logical Equivalences Sets and Set Notation Quantification An Introduction to Vector Spaces The Vector Space R2-The Basics The Vector Space R2-Beyond the Basics The Vector Spaces Rn-The Basics The Vector Spaces Rn-Beyond the Basics The Vector Spaces Rn-Lines and Planes Vector Spaces in General Vector Spaces: Setting the Rules Vector Spaces: On the Wild Side Subspaces Subspaces and Linear Equations Subspaces from Subsets A Numerical Interlude-Systems of Linear Equations Solving Linear Systems Systematic Solutions of Systems Technology and Linear Algebra The Structure of Vector Spaces Spanning Sets Linear Independence More on Linear Independence Linear Independence and Span Vector Space Bases The Dimension of a Vector Space Linear Transformations Transformation Fundamentals Vector Space Isomorphisms Linear Transformations and Matrices Matrix Representations of Transformations Matrices and Associated Vector Spaces Inverses in Matrix Multiplication Elementary Matrices Determinants An Introduction to Determinants Properties of Determinants Eigenvalues and Eigenvectors Eigenvalues, Eigenvectors, and Eigenspaces More on Eigenvalues, Eigenvectors, and Eigenspaces Forests, Digraphs, and PageRank Diagonalization Answers to Selected Problems Indexshow more