unit square

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A square of side 1 unit. Specifically the unit square defined by O (0, 0), I (1, 0), K (1, 1), J (0, 1) is of interest in matrix transformations in the plane. It can be used to identify the transformation from a matrix, or find the matrix if the transformation is known because the images of points I and J form the columns of the matrix which performs that transformation. For example, in a rotation of 90° clockwise (about the origin), the image of I is (0, −1) and the image of J is (1, 0) so the matrix is . If a matrix of a transformation is then the image of I is just the first column, i.e. (1, 0), so it has not moved, and the image of J is (3, 1), so the transformation is a shear parallel to the x-axis which moves (0, 1) to (3, 1).

Subjects: Mathematics.

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