Abstract

BETANCUR SANCHEZ, Alexander; ROA FUENTES, Solange  and  BALLESTEROS, Silvia Juliana. A preliminary genetic decomposition of the concept of eigenvalue and eigenvector: the analysis of textbooks as a substrate in the construction of cognitive models. Relime [online]. 2021, vol.24, n.3, pp.245-276.  Epub Sep 19, 2022. ISSN 2007-6819.  https://doi.org/10.12802/relime.21.2431.

In APOS theory (Action, Process, Object, Scheme), the design of a genetic decomposition is the result of Theoretical Analysis (first component of the theory’s research cycle) where textbook analysis is one of the elements to be considered. However, as of the date of this report, there are no publications on how to perform textbook analysis and the process behind the construction of a genetic decomposition. In this writing, the criteria proposed by Campos (2017) are used to analyze three linear algebra textbooks, specifically in relation to the concept of eigenvalue and eigenvector along with a methodology that accounts for the design of a preliminary genetic decomposition for the concept of eigenvalue and eigenvector on linear operators considering: the input of textbook analysis, existing research reports and the experience of researchers as teachers and students.

Keywords : Eigenvalues and Eigenvectors; APOS Theory; Genetic decomposition; Textbook.

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