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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

Silva CJ;
Soares WA;
Galdino SML;
Silva JD;
Medeiros JCO

Cícero José da Silva

Willames de Albuquerque Soares

Sérgio Mário Lins Galdino

Jornandes Dias da Silva

Juan Carlos Oliveira de Medeiros


Keywords

Teacher Training
Educational Technology
Artificial Intelligence
Digital Literacy

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 : Hk (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


Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2024 Cícero José da Silva , Willames de Albuquerque Soares, Sérgio Mário Lins Galdino, Jornandes Dias da Silva , Juan Carlos Oliveira de Medeiros

Author(s)

  • Cícero José da Silva
  • Willames de Albuquerque Soares
  • Sérgio Mário Lins Galdino
  • Jornandes Dias da Silva
  • Juan Carlos Oliveira de Medeiros