Relationship of polygon areas in geometric linear transformations
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Abstract
In the present investigation, a revision of previous concepts such as, Vector Spaces, Linear Transformations and Associated Matrices is carried out; particularly the study focuses on geometric transformations. Then, several examples are made verifying the relationship between existing areas in polygons obtained from a geometric transformation to raise a conjecture about that relationship. Finally, it demonstrates the conjecture based on a transformation between parallelograms in order to make an extension to any polygon with the use of the calculation of areas in the plane.
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How to Cite
Relationship of polygon areas in geometric linear transformations. (2025). Identidad Bolivariana, 9(1), 102-117. https://doi.org/10.37611/IB9ol1102-117
References
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B. Kolman; Álgebra Lineal; Pearson Education; México 2012.
F. Hohn; Elementary Matrix Algebra; The Macmillan Company; USA 1961.
M. Giaquinta; Mathematical Analysis; Birkhauser; USA 2007.
T. Apostol; Mathematical Analysis; Addison-Wesley Publishing Company; Inglaterra 1960.
J. C. Bressan; Interpretación geométrica de la regla de Cramer; Argentina 2008.
J. G. Molina; Concepciones de la transformación lineal en el contexto geométrico; México 2006