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Linear Algrebra: A Geometric Approach de Malcolm R. Adams

Linear Algrebra: A Geometric Approach

Autor Malcolm R. Adams, Theodore Shifrin
en Limba Engleză Hardback – 30 iun 2010
"Linear Algebra: A Geometric Approach, Second Edition," presents the standard computational aspects of linear algebra and includes a variety of intriguing interesting applications that would be interesting to motivate science and engineering students, as well as help mathematics students make the transition to more abstract advanced courses. The text guides students on how to think about mathematical concepts and write rigorous mathematical arguments.
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Specificații

ISBN-13: 9781429215213
ISBN-10: 1429215216
Pagini: 372
Dimensiuni: 203 x 254 x 23 mm
Greutate: 1.02 kg
Ediția:Revizuită
Editura: MACMILLAN EDUCATION
Locul publicării:New York, United States

Descriere

Linear Algebra: A Geometric Approach, Second Edition, is a text that not only presents the standard computational aspects of linear algebra and interesting applications, it guides students to think about mathematical concepts and write rigorous mathematical arguments. This thought-provoking introduction to the subject and its myriad applications is interesting to the science or engineering student but will also help the mathematics student make the transition to more abstract advanced courses. The second edition has been updated with additional examples and exercises and has been streamlined for easier teaching and studying.

Cuprins

Preface
Foreword to the Instructor
Foreword to the Student
Chapter 1. Vectors and Matrices
1. Vectors
2. Dot Product
3. Hyperplanes inRn
4. Systems of Linear Equations and Gaussian Elimination
5. The Theory of Linear Systems
6. Some Applications
Chapter 2. Matrix Algebra
1. Matrix Operations
2. Linear Transformations: An Introduction
3. Inverse Matrices
4. Elementary Matrices: Rows get Equal Time
5. The Transpose
Chapter 3. Vector Spaces
1. Subspaces of Rn
2. The Four Fundamental Subspaces
3. Linear Independence and Basis
4. Dimension and Its Consequences
5. A Graphic Example
6. Abstract Vector Spaces
Chapter 4. Projections and Linear Transformations
1. Inconsistent Systems and Projection
2. Orthogonal Bases
3. The Matrix of a Linear Transformation and the Change-of-Basis Formula
4. Linear Transformations on Abstract Vector Spaces
Chapter 5. Determinants
1. Properties of Determinants
2. Cofactors and Cramer’s Rule
3. Signed Area inR2and Signed Volume inR2
Chapter 6. Eigenvalues and Eigenvectors
1. The Characteristic Polynomial
2. Diagonalizability
3. Applications
4. The Spectral Theorem
Chapter 7. Further Topics
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations
For Further Reading
Answers to Selected Exercises
List of Blue Boxes
Index

Notă biografică

MALCOLM ADAMS, University of Georgia, USA.

THEODORE SHIFRIN, University of Georgia, USA.

Caracteristici


Solid introduction
Thought-provoking, with plenty of examples and exercises
Updated and streamlined for easier teaching and studying