Orthogonal Projections and Applications in Linear Algebra (UMAP)

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