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Product No. 99756 Supplementary Print Price: FREE with membership
 

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 Gram-Schmidt 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 Three-Dimensional Computer Graphics
Application to Ordinary Least-Squares 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
Gram-Schmidt Orthogonalization

SUMMARY OF ORTHOGONAL PROJECTIONS

CONCLUSION

SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHOR