Shear mapping, also known as shear transformation, is a type of linear transformation that distorts the shape of an object by shifting its points in a specific direction, while leaving the other dimensions unchanged. In a shear mapping, lines that are parallel remain parallel, and the angles between lines can change, but the lengths of the lines themselves do not change. In two dimensions, a shear mapping can be represented by a shear matrix.
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A horizontal shear fixes the horizontal axis pointwise and sends to . Its determinant is one and both eigenvalues are one. A nonzero shear preserves area but generally changes lengths and angles. Composing a shear with a planar rotation can produce a symmetric stretch; having determinant one alone does not make a linear map a shear.