Relationship of polygon areas in geometric linear transformations

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.