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Orthogonal Projections and Applications in Linear Algebra (UMAP)
Yves Nievergelt

Mathematics Topic: Linear Algebra 
Application Areas: Computer science, engineering, differential equations, statistics 
Prerequisites: General inner products and GramSchmidt orthogonalization in general linear spaces. 

 ©1998 by COMAP, Inc.  Tools for Teaching 1997  30 pages 

This module demonstrates how real applications require orthogonal projections in abstract linear spaces. The material presented here may serve either as a complement within a first course in linear algebra or as a review in a subsequent course, for instance, in computer graphics, numerical analysis, or Fourier analysis.
Table of Contents:
INTRODUCTION
APPLICATIONS OF ORTHOGONAL PROJECTIONS
Application to ThreeDimensional Computer Graphics
Application to Ordinary LeastSquares Regression
Application to the Computation of Functions
Application to Fourier Series and Transforms
SUMMARY OF DEFINITIONS AND THEOREMS
Number Fields
Linear Spaces
Inner Products and Inequalities
GramSchmidt Orthogonalization
SUMMARY OF ORTHOGONAL PROJECTIONS
CONCLUSION
SOLUTIONS TO THE EXERCISES
REFERENCES
ABOUT THE AUTHOR



