Elementary Linear Algebra, 7/e
Bernard Kolman, Drexel Univesity
David R. Hill, Temple University
Published September, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 568 pp.
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Introductory Linear Algebra-Mathematics
Linear Algebra-Mechanical Engineering
For first courses in Linear Algebra or Matrix Theory.
This introductory text offers a fine balance between
abstraction/theory and computational skills. While vector spaces come
early, this is not a heavy duty theory text. This edition is more
applied than ever before.
NEWNew topics addede.g., dynamical
systems (Sec. 7.2), spectral decomposition and singular value decomposition
NEWMaterial expanded in some sectionse.g.,
NEWMore careful, step-by-step treatment
of eigenvalues and eigenvectors.
NEWGreater use of linear combinations-of-columns
approachAs a running theme throughout the book.
NEWMore exercises, at all levelsSome
are more open-ended, allowing for exploration and discovery.
NEWMore geometry addedi.e., offers
a stronger emphasis on the geometrical presentation of basic ideas
and supports this emphasis with an increased use of illustrative figures.
NEWA chapter on MATLAB (Ch. 8)Provides
an introduction to MATLAB. Ch. 9 consists of exercises that are specially
designed to be solved using MATLAB.
Strong pedagogical frameworkNew topics gradually
introduced by connecting abstract ideas to concrete foundations.
Specially marked, software-neutral, computer exercisesThese
optional problems are found throughout chapters 1-7 and enable the
use of Maple, etc. as opposed to chapter 9, which focuses on MATLAB
Supplementary Text Linear Algebra Labs with MATLAB, 2/e,
by Hill and Zitarelli is available at a 50% discount when packaged
with the textProvides labs and applications of material drawn
from the text.
1. Linear Equations and Matrices.
Systems of Linear Equations. Matrices; Matrix Operations.
Algebraic Properties of Matrix Operations. Special Types of Matrices
and Partitioned Matrices. Echelon Form of a Matrix. Elementary Matrices;
Finding A^-1. Equivalent Matrices. LU-Factorization. Supplementary
2. Real Vector Spaces.
Vectors in the Plane and In 3-Space. Vector Spaces. Subspaces.
Span and Linear Independence. Basis and Dimension. Homogeneous Systems.
Coordinates and Isomorphisms. Rank of a Matrix. Supplementary Exercises.
3. Inner Product Spaces.
Standard Inner Product on R^2 and R^3.
Cross Product in R^3 (Optional). Inner Product Spaces. Gram-Schmidt
Process. Orthogonal Complements. Least Squares (Optional). Supplementary
4. Linear Transformations and Matrices.
Definition and Examples. Kernel and Range of a Linear Transformation.
Matrix of a Linear Transformation. Vector Space of Matrices and Vector
Space of Linear Transformations (Optional). Similarity. Computer Graphics
(Optional). Supplementary Exercises.
Definition. Properties of Determinants. Cofactor Expansion.
Inverse of a Matrix. Other Applications of Determinants. Determinants
from a Computational Point of View. Supplementary Exercises.
6. Eigenvalues and Eigenvectors.
Eigenvalues and Eigenvectors. Diagonalization and
Similar Matrices. Stable Age Distribution in a Population; Markov
Processes (Optional). Diagonalization of Symmetric Matrices. Spectral
Decomposition and Singular Value Decomposition (Optional). Real Quadratic
Forms. Conic Sections. Quadric Surfaces. Supplementary Exercises.
7. Differential Equations (Optional).
Differential Equations. Dynamical Systems.
8. MATLAB for Linear Algebra.
Input and Output in MATLAB. Matrix Operations in MATLAB.
Matrix Powers and Some Special Matrices. Elementary Row Operations
in MATLAB. Matrix Inverses in MATLAB. Vectors in MATLAB. Applications
of Linear Combinations in MATLAB. Linear Transformations in MATLAB.
MATLAB Command Summary.
9. MATLAB Exercises.
Appendix A: Preliminaries.
Appendix B: Complex Numbers.
Complex Numbers. Complex Numbers in Linear Algebra.
Answers to Odd-Numbered Exercises.