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