PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Student Understanding of Linear Combinations of Eigenvectors
Page: 1372
Student understanding of eigenspace seems to be a particularly understudied aspect of research on eigentheory. To further detail student understanding of eigenspace relationships, we present preliminary results regarding students’ reasoning on problems involving linear combinations of eigenvectors in which the resultant vector is or is not an eigenvector of the matrix. We detail three preliminary themes gleaned from our analysis: (a) using the phrase “is a linear combination of” to support both correct and incorrect answers; (b) conflating scalars in a linear combination with eigenvalues, and (c) reasoning about the dimension of eigenspaces versus a number of eigenvectors.