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Matrices

1 Feb 2017, 17:09 UTC
Matrices
(200 words excerpt, click title or image to see full post)

I enjoy linear algebra. I use it in making polyhedra and drawings. Here are a few visualizations of matrices. To keep it simple I use 2x2 matrices. 2x2 matrices act on vectors. The vertices of polygons in a plane can be described vectors, so these same transformations can be done to polygons that dwell in a plane.Rotation MatrixRotating a polygon doesn't change it's area. The area remains the same. The determinant of this matrix is 1.Proportional Scaling MatrixDoubling size as well as height boosts a polygon's area by a factor of four. This determinant of this matrix is 4.Non Proportional Scaling MatrixThis matrix stretches the width to twice the original and squeezes the height to half of what it was. Overall the area is unchanged. The determinant of this matrix is 1.Shear or Skew MatrixWhen I was using Macromedia Freehand, the graphics program called this transformation "skew". Then Adobe ate Macromedia and I was forced to use Adobe Illustrator. Illustrator calls it "shear".This transformation transforms a horizontally aligned rectangle to a parallelogram with same base and height. Area remains unchanged. The determinant of this matrix is 1.Flip MatrixMaking the first term in the main diagonal negative flips polygons about the ...

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