Matrix Transformations and Their Geometric Effects in 2D Space
DOI:
https://doi.org/10.65420/cjhes.v1i1.8Keywords:
Matrix transformation, linear algebra, 2D geometry, scaling, rotation, shear, projection, eigenvalues, computer graphicsAbstract
This paper explores linear transformations in two-dimensional space, focusing on how 2×2 matrices act on vectors and shapes. We review definitions of vectors and matrices, then examine common transformations: scaling, rotation, reflection, shear, and projection. Each type’s matrix form and effect on points are given, with example equations. We show how basic shapes (square, triangle, circle) change under transforms, and discuss eigenvalues and invariant directions. Composition of transforms (matrix multiplication) is explained, noting that the order matters. Applications in computer graphics, physics, and robotics are highlighted. Figures and tables summarize key transformations, and practice problems are provided. Overall, we emphasize visualization and intuitive understanding of how matrices warp the plane.
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