A look at the composition of linear transformations in the language of matrices, some types of matrices of order 2 represented geometrically in the R2 plane

Abstract

The purpose of this note is to present compositions of linear transformations in  the language of matrices, as well as to present geometric interpretations for some particular cases of order 2 matrices such as reflections around the x and y axes, reflections around the origin, contraction, expansion or homothetic, horizontal and vertical shear, counterclockwise rotation, orthogonal projection of u = (x,  y) on the line G : y = ax, a /= 0, as well as the reflection of the same vector around this same line. It is worth mentioning that your compositions in the language of matrices is a first model of computer graphics. Illustratively, for example, the expansion of factor k : H_k (x, y) = (kx, ky) or in the language of matrices, represents a computer zoom by zooming if k > 1 or contracting if 0 < k < 1.

DOI:https://doi.org/10.56238/sevened2024.001-064