Knop Linear Algebra

A First Course with Applications
1. Auflage 2011
ISBN: 978-1-58488-783-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 752 Seiten

Reihe: Textbooks in Mathematics

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™, MATLAB®, 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.

Zielgruppe

Undergraduate students of mathematics, science, engineering, and economics; high school students of AP mathematics.

Autoren/Hrsg.

Knop, Larry E.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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
Index