Linear Algebra with Applications
2nd Edition
Published on 12. November 1996
Book
Hardback
512 pages
978-0-673-99386-1 (ISBN)
Description
This clear, unintimidating introductory text is distinguished by its strong computational and applied approach. Suitable for a sophomore-level course in linear, matrix, or computational algebra, it prepares students for further study in mathematics, computer science, chemistry, or economics. An outstanding interactive software package, specifically developed to accompany this text, offers ease of use, power, and flexibility, focusing attention on the interpretation of calculations rather than on the calculations themselves. The Second Edition has been improved by including more applications, more motivation to discussions, more graphics, and discussions of various relevant software packages, and the TI-85 graphics calculator.
More details
Other editions
Previous edition
Charles G. Cullen
Linear Algebra with Applications
Book
04/1988
Longman Higher Education
€49.46
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Content
1. Linear Systems and Matrices.
Geometric View of Linear Systems.
Gaussian and Gauss-Jordan Elimination.
Row Equivalence and Echelon Matrices.
Homogeneous Systems.
Matrix Algebra.
Properties of Matrix Operations.
Row Equivalence and Matrix Multiplication.
The LU Factorization (Optional)
Partial Pivoting (Optional).
2. Determinants.
Definitions and Examples.
Evaluation of det (A): A Better Way.
Additional Properties of Determinants.
Eigenvalues and Eigenvectors.
3. Vector Spaces.
R2 and R3: Old Friends.
Euclidean n-space and its Subspaces.
Subspaces of Rn -continued.
Linear Independence and Dependence in Rn.
Basis and Dimension.
Orthogonality in Rn.
Vector Spaces-The General Concept.
Subspaces.
Linear Independence, Basis, and Dimension.
4. Linear Transformations.
Definitions and Examples.
The Range and Null Space of a Linear Transformation.
The Algebra of Linear Transformations.
Geometric Interpretation.
Matrices and Linear Transformations.
Change of Basis (Optional).
The Change-of-Basis Problem (Optional).
5. Similar Matrices and The Eigenvalue Problem.
Diagonalization-Eigenvalues and Eigenvectors.
Orthogonal Similarity and Symmetric Matrices.
Schur's Theorem (Optional).
The Power Method (Optional).
6. Linear Programming.
The Geometric Point of View.
Different Types of Linear Programming Problems.
The Simplex Method.
Refinements of the Simplex Method.
7. Selected Applications.
Graph theory.
Least Squares Approximations.
Quadratic Forms.
Linear Economic.
Appendices.
Linear Algebra Software.
The Matman Program.
The Matalg Program.
The Matlab Program.
Appendices.
Answers to Odd Numbered Exercises.
Index.
Geometric View of Linear Systems.
Gaussian and Gauss-Jordan Elimination.
Row Equivalence and Echelon Matrices.
Homogeneous Systems.
Matrix Algebra.
Properties of Matrix Operations.
Row Equivalence and Matrix Multiplication.
The LU Factorization (Optional)
Partial Pivoting (Optional).
2. Determinants.
Definitions and Examples.
Evaluation of det (A): A Better Way.
Additional Properties of Determinants.
Eigenvalues and Eigenvectors.
3. Vector Spaces.
R2 and R3: Old Friends.
Euclidean n-space and its Subspaces.
Subspaces of Rn -continued.
Linear Independence and Dependence in Rn.
Basis and Dimension.
Orthogonality in Rn.
Vector Spaces-The General Concept.
Subspaces.
Linear Independence, Basis, and Dimension.
4. Linear Transformations.
Definitions and Examples.
The Range and Null Space of a Linear Transformation.
The Algebra of Linear Transformations.
Geometric Interpretation.
Matrices and Linear Transformations.
Change of Basis (Optional).
The Change-of-Basis Problem (Optional).
5. Similar Matrices and The Eigenvalue Problem.
Diagonalization-Eigenvalues and Eigenvectors.
Orthogonal Similarity and Symmetric Matrices.
Schur's Theorem (Optional).
The Power Method (Optional).
6. Linear Programming.
The Geometric Point of View.
Different Types of Linear Programming Problems.
The Simplex Method.
Refinements of the Simplex Method.
7. Selected Applications.
Graph theory.
Least Squares Approximations.
Quadratic Forms.
Linear Economic.
Appendices.
Linear Algebra Software.
The Matman Program.
The Matalg Program.
The Matlab Program.
Appendices.
Answers to Odd Numbered Exercises.
Index.