Didactic Study of the Eigenvalue Concept and Its Geometric Representation in Linear Algebra Learning

Abstract

Students’ understanding of eigenvalues and eigenvectors in linear algebra continues to demonstrate a strong procedural tendency, with insufficient emphasis on structural and geometric meaning. The research gap lies in the limited conceptual studies that systematically reconstruct the eigenvalue concept as an invariant structure by integrating symbolic, geometric, and applicative representations. To address this gap, this research employs a systematic conceptual review approach with stages of literature identification, selection based on inclusion-exclusion criteria, thematic coding, and conceptual modeling. From 45 articles identified in the initial stage, 28 articles passed selection based on title and abstract, 15 articles fully met the inclusion criteria, and 9 articles were analyzed in-depth in the conceptual synthesis. The synthesis results reveal a trend of dominance in computational approaches to eigenvalue learning, weak integration of multiple representations, and minimal geometric exploration before algebraic formalization is introduced. Based on these findings, a cyclic conceptual model is proposed that integrates multi-representation exploration, axiomatic formalization, relational integration between concepts, and reconceptualization in new contexts. This research provides a theoretical foundation for developing more meaningful learning designs, but is limited to literature analysis without direct empirical testing, so validation through quantitative or qualitative research is needed in subsequent stages to test the effectiveness of the proposed model in improving students’ conceptual understanding in linear algebra courses.