Using Fractals to Motivate Linear Algebra (UMAP)
Author: Brian Habecker, Annalisa Crannell
We introduce a project that encourages the reader to "adopt" a fractal and then find out "everything" about it. We lead the reader through the concepts needed for the project: affine transformations, matrix notation and multiplication, determinants, eigenvalues and eigenvectors, and Hausdorff dimension. We refer the reader to relevant technology and software.
Table of Contents:
INTRODUCTION
WHAT IS A FRACTAL?
AFFINE TRANSFORMATIONS
UNDERSTANDING ITERATIONS VISUALLY
MATRIX AND VECTOR NOTATION
AREAS OF IMAGES OF THE ORIGINAL SQUARE
EIGENVALUES AND EIGENVECTORS
HAUSDORFF DIMENSION
SOFTWARE
SOLUTIONS TO THE EXERCISES
APPENDIX: FRACTALS FOR THE PROJECT ASSIGNMENT
REFERENCES
ABOUT THE AUTHORS
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