Principles of Linear Algebra with Maple

ISBN-10: 0470637595
ISBN-13: 9780470637593
Edition: 2010
List price: $106.00
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Description: Linear Algebra with Maple (R) uniquely addresses the quickly growing intersection between subject theory and numerical computation. Computer algebra systems such as Maple are becoming ever more powerful, useful, user friendly and readily available  More...

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Book details

List price: $106.00
Copyright year: 2010
Publisher: John Wiley & Sons, Limited
Publication date: 10/22/2010
Binding: Hardcover
Pages: 616
Size: 6.50" wide x 9.50" long x 1.50" tall
Weight: 2.2
Language: English

Linear Algebra with Maple (R) uniquely addresses the quickly growing intersection between subject theory and numerical computation. Computer algebra systems such as Maple are becoming ever more powerful, useful, user friendly and readily available to the average student and professional, but thre are few books which currently cross this gap between linear algebra and Maple. This book introduces algebra topics which can only be taught with the help of computer algebra systems, and the authors include all of the commands required to solve complex and computationally challenging linear algebra problems using Maple. The book begins with an introduction to the commands and programming guidelines for working with Maple. Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramerrs"s rule. Basic linear algebra topics, such as vectors, dot product, cross product, vector projection, are explored as well as the more advanced topics of rotations in space, rolling a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear programming, linear transformations from R n to R m , the geometry of linear and affine transformations, and least squares fits and pseudoinverses. Although computational in nature, the material is not presented in a simply theory-proof-problem format. Instead, all topics are explored in a reader-friendly and insightful way. The Maple software is fully utilized to highlight the visual nature of the topic, as the book is complete with numerous graphics in two and three dimensions, animations, symbolic manipulations, numerical computations, and programming. Exercises are supplied in most chapters, and a related Web site houses Maple code so readers can work throug the provided examples.

Preface
Conventions and Notations
An Introduction To Maple�
The Commands
Programming
Linear Systems of Equations and Matrices
Linear Systems of Equations
Augmented Matrix of a Linear System and Row Operations
Some Matrix Arithmetic
Gauss-Jordan Elimination and Reduced Row Echelon Form
Gauss-Jordan Elimination and rref
Elementary Matrices
Sensitivity of Solutions to Error in the Linear System
Applications of Linear Systems and Matrices
Applications of Linear Systems to Geometry
Applications of Linear Systems to Curve Fitting
Applications of Linear Systems to Economics
Applications of Matrix Multiplication to Geometry
An Application of Matrix Multiplication to Economics
Determinants, Inverses, and Cramer's Rule
Determinants and Inverses from the Adjoint Formula
Determinants by Expanding Along Any Row or Column
Determinants Found by Triangularizing Matrices
LU Factorization
Inverses from rref
Cramer's Rule
Basic Linear Algebra Topics
Vectors
Dot Product
Cross Product
Vector Projection
A Few Advanced Linear Algebra Topics
Rotations in Space
"Rolling" a Circle Along a Curve
The TNB Frame
Independence, Basis, and Dimension for Subspaces of R<sup>n</sup>
Subspaces of R<sup>n</sup>
Independent and Dependent Sets of Vectors in R<sup>n</sup>
Basis and Dimension for Subspaces of R<sup>n</sup>
Vector Projection onto a Subspace of R<sup>n</sup>
The Gram-Schmidt Orthonormalization Process
Linear Maps from R<sup>n</sup> to R<sup>n</sup>
Basics About Linear Maps
The Kernel and Image Subspaces of a Linear Map
Composites of Two Linear Maps and Inverses
Change of Bases for the Matrix Representation of a Linear Map
The Geometry of Linear and Affine Maps
The Effect of a Linear Map on Area and Arclength in Two Dimensions
The Decomposition of Linear Maps into Rotations, Reflections, and Rescalings in R<sup>2</sup>
The Effect of Linear Maps on Volume, Area, and Arclength in R<sup>3</sup>
Rotations, Reflections, and Rescalings in Three Dimensions
Affine Maps
Least-Squares Fits and Pseudoinverses
Pseudoinverse to a Nonsquare Matrix and Almost Solving an Overdetermined Linear System
Fits and Pseudoinverses
Least-Squares Fits and Pseudoinverses
Eigenvalues and Eigenvectors
What Are Eigenvalues and Eigenvectors, and Why Do We Need Them?
Summary of Definitions and Methods for Computing Eigenvalues and Eigenvectors as well as the Exponential of a Matrix
Applications of the Diagonalizability of Square Matrices
Solving a Square First-Order Linear System of Differential Equations
Basic Facts About Eigenvalues, Eigenvectors, and Diagonalizability
The Geometry of the Ellipse Using Eigenvalues and Eigenvectors
A Maple Eigen-Procedure
Suggested Reading
Indices
Keyword Index
Index of Maple Commands and Packages

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