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Any such mapping can be called shear transformation, transvection, or just shearing. The transformations will be applied with a shear matrix or transvection, an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity matrix and changing one of the zero parts with a non-zero value. On this case, the displacement is horizontal by an element of two the place the fixed line is the x-axis, and the signed distance is the y-coordinate. Note that points on reverse sides of the reference line are displaced in reverse directions. Shear mappings must not be confused with rotations. Applying a shear map to a set of factors of the airplane will change all angles between them (besides straight angles), and the size of any line segment that is not parallel to the direction of displacement. Therefore, it should often distort the form of a geometric determine, for example turning squares into parallelograms, and circles into ellipses.

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