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单词 unit square
释义

unit square

A square of side 1 unit, specifically the unit square defined by O(0,0), I(1,0), K(1,1), J(0,1). It can be used to identify the linear map from a matrix or find the matrix if the linear map 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 inline. If a matrix of a transformation is inline 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).

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更新时间:2025/4/29 20:42:21