Elementary Linear Algebra with Applications

by Richard Hill

• ISBN13: 9780030103476
• ISBN10: 0030103479
• Edition: 3rd
• Format: Hardcover
• Copyright: 1995-09-08
• Publisher: Cengage Learning
• More Book Details

About This Book

Elementary Linear Algebra with Applications, 3rd Edition

This book is a comprehensive guide to the fundamental concepts of linear algebra, designed to develop students' geometric intuition as a foundation for learning the concepts of span and linear independence. It's a go-to resource for students and educators alike, offering a detailed exploration of linear algebra principles and meeting scope and sequence requirements for typical introductory linear algebra courses.

Who Uses It?

Primarily, this book is used by students and instructors in introductory linear algebra courses at the college and university levels. It's also a valuable resource for anyone interested in understanding the basics of linear algebra, including professionals looking to refresh their knowledge or expand their understanding of mathematical principles.

History and Editions

The 3rd edition of Elementary Linear Algebra with Applications has been a staple in the field since its publication in 1996. This edition includes detailed updates on various linear algebra topics, such as Gaussian elimination, determinants, and matrix operations. It also includes a list of applications that illustrate the practical use of linear algebra in real-world scenarios.

Author and Other Works

The author of Elementary Linear Algebra with Applications is Richard O. Hill. Richard Hill is known for his clear and concise explanations of complex mathematical concepts, making this book an excellent choice for students of all levels. While specific details about other books written by Richard Hill are not readily available, his dedication to making linear algebra accessible to a broad audience is evident in this edition.

Detailed Information

ISBNs and Formats

Hardcover: ISBN-13: 9780030103476

eTextbook: ISBN-13: 9780030103476 (The ebook for "Elementary Linear Algebra with Applications, 3rd Edition" is available right here on eCampus.com!)

Loose-leaf: Not available

Rental Options: Available through eCampus.com with various rental durations

Publication Details

Publisher: Saunders College Publishing

Publication Date: 1996

Number of Pages: 445

Language: English

Other Editions and Formats

10th Edition: Not available

11th Edition: Not available

12th Edition: Not available

Related ISBNs:

9780030103476 (The ebook for "Elementary Linear Algebra with Applications, 3rd Edition" is available right here on eCampus.com!)

9780030103476 (The ebook for "Elementary Linear Algebra with Applications, 3rd Edition" is available right here on eCampus.com!)

Note: Since the book is primarily available in hardcover and e-textbook formats, the above ISBNs are listed to ensure accuracy and clarity.

Rental Options

Rental options are available through eCampus.com with various rental durations, making it convenient for students to access this essential resource without the long-term commitment of purchasing.

Table of Contents

Preface. List of Applications. 1. Introduction to Linear Equations and Matrices. Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises. 2. Determinants. The Determinant Function. Properties of Determinants. Finding det A Using Signed Elementary Products. Cofactor Expansion: Cramer's Rule. Applications. Review Exercises. 3. Vector Spaces. Vectors in 2- and 3-Spaces. Euclidean n-Space. General Vector Spaces. Subspaces, Span, Null Spaces. Linear Independence. Basis and Dimension. The Fundamental Subspaces of a Matrix; Rank. Coordinates and Change of Basis. An Application: Error-Correcting Codes. Review Exercises. Cumulative Review Exercises. 4. Linear Transformations, Orthogonal Projections and Least Squares. Matrices as Linear Transformation. Relationships Involving Inner Products. Least Squares and Orthogonal Projections. Orthogonal Bases and the Gram-Schmidt Process. Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited). Encoding the QR Decompositions: A Geometric Approach. General Matrices of Linear of Linear Transformations; Similarity. Review Exercises. Cumulative Review Exercises. 5. Eigenvectors and Eigenvalues. A Brief Introduction to Determinants. Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices. An Application - Difference Equations: Fibonacci Sequences and Markov Processes. An Application -Differential Equations. An Application -- Quadratic Forms. Solving the Eigenvalue Problem Numerically. Review Exercises. Cumulative Review Exercises. 6. Further Directions. Function Spaces. The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems. Iterative Method. Matrix Norms. General Vector Spaces and Linear Transformations Over an Arbitrary Field. Review Exercises. Appendix A: More on LU Decompositions. Appendix B: Counting Operations and Gauss-Jordan Elimination. Appendix C: Another Application. Appendix D: Introduction to MATLAB and Projects. Bibliography and Further Readings. Index.