## Elementary Linear Algebra, 7/e

Bernard Kolman, Drexel Univesity
David R. Hill, Temple University

Published September, 1999 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-085199-X

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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.

NEW—New topics added—e.g., dynamical systems (Sec. 7.2), spectral decomposition and singular value decomposition (Sec. 6.5).
NEW—Material expanded in some sections—e.g., linear transformations.
NEW—More careful, step-by-step treatment of eigenvalues and eigenvectors.
NEW—Greater use of linear combinations-of-columns approach—As a running theme throughout the book.
NEW—More exercises, at all levels—Some are more open-ended, allowing for exploration and discovery.
NEW—More geometry added—i.e., offers a stronger emphasis on the geometrical presentation of basic ideas and supports this emphasis with an increased use of illustrative figures.
NEW—A 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 framework—New topics gradually introduced by connecting abstract ideas to concrete foundations. Specially marked, software-neutral, computer exercises—These optional problems are found throughout chapters 1-7 and enable the use of Maple, etc. as opposed to chapter 9, which focuses on MATLAB exclusively.
Supplementary Text Linear Algebra Labs with MATLAB, 2/e, by Hill and Zitarelli is available at a 50% discount when packaged with the text—Provides 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 Exercises.

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 Exercises.

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.

5. Determinants.

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.

Sets. Functions.

Appendix B: Complex Numbers.

Complex Numbers. Complex Numbers in Linear Algebra.