A Study of Physics Students' Interpretation of Matrix Multiplication

As part of a multi-year project to investigate student use of mathematics in upper-division physics, we have studied student reasoning with matrix multiplication. Matrix multiplication and eigentheory are used by physics students in courses including classical mechanics, optics, and quantum mechanics. While there have been recent investigations of student use of linear algebra in physics, prior work has focused largely on quantum mechanics. We have investigated student use of matrix multiplication as a modeling tool as well as the extent to which physics students' interpretations of matrix multiplication were consistent with research in mathematics courses. In particular, we used the categories developed by Larson and Zandieh (2013) to describe math students' interpretations of matrix multiplication: linear combination, system of equations, and transformation reasoning. We examined the responses of physics students to written questions and used the results to develop an interview protocol to examine how physics students interpret matrix equations using the three interpretations to classify their responses. Results are shown from an interview sample of six undergraduate physics majors.