“Well written, concise, good choice of examples, helpful applications, nice organization of topics, and affordable!” — Lloyd Best, Pacific Union College
“The book is very well organized. We appreciate its thoroughness.” — Kristina Sampson, Lone Star College
488 pages, $119.95 list
1-4786-2777-8
978-1-4786-2777-7
© 2009
hardcover
Instructor's Solutions Manual available
eBook availability
Introduction to Linear Algebra with Applications
Over the last few decades, linear algebra has become more relevant than ever. Applications have increased not only in quantity but also in diversity, with linear systems being used to solve problems in chemistry, engineering, economics, nutrition, urban planning, and more. DeFranza and Gagliardi introduce students to the topic in a clear, engaging, and easy-to-follow manner. Topics are developed fully before moving on to the next through a series of natural connections. The result is a solid introduction to linear algebra for undergraduates’ first course.
Outstanding features include:
• Early coverage of vector spaces, providing the abstract theory necessary to understand applications
• Exercises that range from routine to more challenging, extending the concepts and techniques by asking students to construct complete arguments
• Numerous examples designed to develop intuition and prepare readers to think conceptually about topics as they are introduced
• Fact summaries to end each chapter that use nontechnical language to recapitulate details and formulas
Outstanding features include:
• Early coverage of vector spaces, providing the abstract theory necessary to understand applications
• Exercises that range from routine to more challenging, extending the concepts and techniques by asking students to construct complete arguments
• Numerous examples designed to develop intuition and prepare readers to think conceptually about topics as they are introduced
• Fact summaries to end each chapter that use nontechnical language to recapitulate details and formulas
Reactions
1. Systems of Linear Equations and Matrices
Systems of Linear Equations / Matrices and Elementary Row Operations / Matrix Algebra / The Inverse of a Square Matrix / Matrix Equations / Determinants / Elementary Matrices and LU Factorization / Applications of Systems of Linear Equations
2. Linear Combinations and Linear Independence
Vectors in Rn / Linear Combinations / Linear Independence
3. Vector Spaces
Definition of a Vector Space / Subspaces / Basis and Dimension / Coordinates and Change of Basis / Application: Differential Equations
4. Linear Transformations
Linear Transformations / The Null Space and Range / Isomorphisms / Matrix Representation of a Linear Transformation / Similarity / Application: Computer Graphics
5. Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors / Diagonalization / Application: Systems of Linear Differential Equations / Application: Markov Chains
6. Inner Product Spaces
The Dot Product on Rn / Inner Product Spaces / Orthonormal Bases / Orthogonal Complements / Application: Least Squares Approximation / Diagonalization of Symmetric Matrices / Application: Quadratic Forms / Application: Singular Value Decomposition
Systems of Linear Equations / Matrices and Elementary Row Operations / Matrix Algebra / The Inverse of a Square Matrix / Matrix Equations / Determinants / Elementary Matrices and LU Factorization / Applications of Systems of Linear Equations
2. Linear Combinations and Linear Independence
Vectors in Rn / Linear Combinations / Linear Independence
3. Vector Spaces
Definition of a Vector Space / Subspaces / Basis and Dimension / Coordinates and Change of Basis / Application: Differential Equations
4. Linear Transformations
Linear Transformations / The Null Space and Range / Isomorphisms / Matrix Representation of a Linear Transformation / Similarity / Application: Computer Graphics
5. Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors / Diagonalization / Application: Systems of Linear Differential Equations / Application: Markov Chains
6. Inner Product Spaces
The Dot Product on Rn / Inner Product Spaces / Orthonormal Bases / Orthogonal Complements / Application: Least Squares Approximation / Diagonalization of Symmetric Matrices / Application: Quadratic Forms / Application: Singular Value Decomposition