We present an innovative task sequence for an introductory linear algebra course that supports students' reinvention of eigentheory and diagonalization. Grounded in the instructional design theory of Realistic Mathematics Education, the task sequence builds from students' experience with linear transformations in to introduce the idea of stretch factors and stretch directions. This is leveraged towards defining eigenvalues and eigenvectors, reinventing methods to determine them, and connecting them to change of basis and diagonalization. In the poster, we discuss the development of the task sequence and analyses of students' work on the tasks, specifically on characterizing their approaches for developing eigentheory methods.