Introductory Linear Algebra With Applications
by Kolman, Bernard; Hill, David R.Edition: 7th
Format: Hardcover
Pub. Date: 2001-01-01
Publisher(s): Pearson College Div
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Summary
This text provides an introduction to the basic ideas, computational techniques, and applications of linear algebra. The most applied of our basic texts in this market, this text has a superb range of problem sets. Also, this book is extremely technology-friendly, integrating optional CAS and a robust website. Topics covered include wavelets; the Leslie Population Model; fractals; dynamical systems; linear equations and matrices; determinants; vectors; eigenvalues and eigenvectors; linear transformations and matrices; linear programming; and more. Ideal as an introduction to Linear Algebra.
Table of Contents
I. INTRODUCTORY LINEAR ALGEBRA.
1. Linear Equations and Matrices.
2. Determinants.
3. Vectors in R2 and R3.
4. Real Vector Spaces.
5. Eigenvalues and Eigenvectors.
6. Linear Transformations and Matrices.
Cumulative Review of Part I.
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 R3 (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 Rn. 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 Linear Transformation.
Cumulative Review of Part I.
II. OTHER APPLICATIONS.
7. Linear Programming.
8. Applications of Eigenvalues and Eigenvectors.
Appendix A: Introduction to MATLAB.
Appendix B: Complex Numbers.
Appendix C: Further Directions.
Answers to Odd-Numbered Exercises and Chapter Tests.
Index.
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.
Answers to Odd-Numbered Exercises and Chapter Tests.
Index.
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