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Introductory linear algebra with applications.

Author: Bernard Kolman; David R Hill
Publisher: Upper Saddle River, N.J. : Prentice Hall, ©2001.
Edition/Format:   Print book : English : 7th ed.View all editions and formats
Summary:

Designed for undergraduate-level courses, this book provides an applied introduction to the basic ideas, computational techniques and applications of linear algebra. This new edition features new  Read more...

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Details

Document Type: Book
All Authors / Contributors: Bernard Kolman; David R Hill
ISBN: 0130182656 9780130182654 0130337064 9780130337061
OCLC Number: 45008513
Notes: Includes index.
Description: xvi, 577, 68, 10 pages : illustrations ; 27 cm
Contents: Part I. Introductory Linear Algebra --
1. Linear Equations and Matrices --
Linear Systems --
Matrices --
Dot Product and Matrix Multiplication --
Properties of Matrix Operations --
Graph Theory (Optional) --
Solutions of Linear Systems of Equations --
Electrical Circuits (Optional) --
Markov Chains (Optional) --
The Inverse of a Matrix --
Linear Economic Models (Optional) --
Wavelets (Optional) --
LU-Factorization (Optional) --
2. Determinants --
Definition and Properties --
Cofactor Expansion and Applications --
Determinants from a Computational Point of View --
3. Vectors in R2 and R3 --
Vectors in the Plane --
N-Vectors --
Introduction to Linear Transformations --
Computer Graphics --
Computer Graphics (Optional) --
Cross Products in R<W0^>3 (Optional) --
Lines and Planes --
4. Real Vector Spaces --
Real Vector Spaces --
Subspaces --
Linear Independence --
Basis and Dimension --
Homogeneous Systems --
The Rank of a Matrix and Applications --
Coordinates and Change of Basis --
Orthonormal Bases in R<W0^>n --
QR-Factorization (Optional) --
Orthogonal Complements --
Least Squares (Optional) --
5. Eigenvalues and Eigenvectors --
Eigenvalues and Eigenvectors --
Diagonalization and Similar Matrices --
Diagonalization and Symmetric Matrices --
6. Linear Transformations and Matrices --
Definition and Examples --
The Kernel and Range of a Linear Transformation --
The Matrix of a LinearTransformation --
Cumulative Review of Part I --
Part II. Other Applications --
7. Linear Programming --
The Linear Programming Problem --
Geometric Solution --
The Simplex Method --
Duality --
The Theory of Games --
8. Applications of Eigenvalues and Eigenvectors --
The Fibonacci Sequence --
Differential Equations (Calculus Required) --
Dynamical Systems (Calculus Required) --
Intro to Fractals --
Quadratic Forms --
Conic Sections --
Quadric Surfaces --
Appendix A. Introduction to MATLAB --
Appendix B. Complex Numbers --
Complex Numbers --
Complex Numbers in Linear Algebra --
Appendix C. Further Directions --
Inner Product Spaces (Calculus Required) --
Composite and Invertible Linear Transformations.

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