This article presents a teaching proposal that emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. More concretely, these concepts were introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was designed after observing architecture students difficulty grasping the meaning of eigenvectors and eigenvalues from a geometric point of view. The aim of this research is to determine whether the designed teaching proposal allows students to give a geometrical meaning to the concepts of eigenvectors and eigenvalues. To this end, the responses given to a test by the students attending the teaching proposal and others attending a traditional course with no emphasis on visualization were analysed. A classification of the students reasoning was established in order to check differences between both groups. As our findings show, the students who attended the course, where the teaching proposal was developed, obtained better results in questions formulated from a visual point of view than those attending the traditional course. Moreover, it was observed that in the traditional group, no responses reasoned in the embodied world of mathematics were found, whereas in the group attending the teaching proposal responses were found in each of the three worlds of mathematics provided by Tall: embodied, symbolic and formal.