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Linear Functions and Matrix Theory : Textbooks in Mathematical Sciences - Bill Jacob

Linear Functions and Matrix Theory

Textbooks in Mathematical Sciences

Paperback

Published: 30th March 1995
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Courses that study vectors and elementary matrix theory and introduce linear transformations have proliferated greatly in recent years. Most of these courses are taught at the undergraduate level as part of, or adjacent to, the second-year calculus sequence. Although many students will ultimately find the material in these courses more valuable than calculus, they often experience a class that consists mostly of learning to implement a series of computational algorithms. The objective of this text is to bring a different vision to this course, including many of the key elements called for in current mathematics-teaching reform efforts. Three of the main components of this current effort are the following: 1. Mathematical ideas should be introduced in meaningful contexts, with after a clear understanding formal definitions and procedures developed of practical situations has been achieved. 2. Every topic should be treated from different perspectives, including the numerical, geometric, and symbolic viewpoints. 3. The important ideas need to be visited repeatedly throughout the term, with students' understan9ing deepening each time. This text was written with these three objectives in mind. The first two chapters deal with situations requiring linear functions (at times, locally linear functions) or linear ideas in geometry for their understanding. These situations provide the context in which the formal mathematics is developed, and they are returned to with increasing sophistication throughout the text.

Preface
Linear Functions
Linear Geometry
Systems of Linear Equations
Basic Matrix Algebra
Key Concepts of Linear Algebra in R[superscript n]
More Vector Geometry
Eigenvalues and Eigenvectors of Matrices
Matrices as Linear Transformations
Orthogonality and Least-Squares Problems
Answers to Odd-Numbered Problems
Index
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387944517
ISBN-10: 0387944516
Series: Textbooks in Mathematical Sciences
Audience: General
Format: Paperback
Language: English
Number Of Pages: 330
Published: 30th March 1995
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.34 x 17.73  x 1.65
Weight (kg): 0.54