Application-Inspired Linear Algebra

Heather A. Moon received her PhD in Mathematics at Washington State University. She spent 8 years as an Assistant/Associate Professor of Mathematics at liberal arts colleges, where she mentored numerous undergraduate research projects in data and image analysis.  Currently, she is pursuing her scientific interests, in the doctoral program in Physics at Washington State University, where she is excited to use her expertise in mathematics and data and image analysis to study the world around us.Thomas J. Asaki received his Ph.D. in Physics at Washington State University.  He spent 13 years as a postdoc and technical staff member at Los Alamos National Laboratory exploring inverse problems, image and data analysis methods, nondestructive acoustic testing and related optimization problems.  He is currently an Associate Professor in the Department of Mathematics and Statistics at Washington State University where, since 2008, he has enjoyed continuing research and helping students discover richness in applied mathematics.Marie Snipes received her Ph.D. in Mathematics from the University of Michigan.  Prior to her doctoral studies, she spent four years in the US Air Force as a data analyst.  She is currently an Associate Professor of Mathematics at Kenyon College, where she regularly teaches inquiry-based courses and mentors undergraduate research projects.  Her research interests include geometric function theory, analysis in metric spaces, and applications of these areas to data problems.The authors are co-creators of the IMAGEMath Project (www.imagemath.org), bringing image and data applications (of calculus of variations, PDE's, and linear algebra) into the undergraduate curriculum.

• 1 Introduction.- 2 Vector Spaces.- 3 Vector Space Arithmetic and Representations.- 4 Linear Transformations.- 5 Invertibility.- 6 Diagonalization.- 7 Inner Product Spaces and Pseudo-Invertibility.- 8 Conclusions.- A Radiography and Tomography.- B The Diffusion Equation.- C Proof Techniques.- D Fields.