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# Shear

Shear is a form of structural failure. A component fails by shearing when it splits into two parts that slide past each other. See shear stress.

In mathematics, a shear is a particular kind of linear mapping. For a vector space V and subspace W, a shear fixing W translates all vectors parallel to W. To be more precise, if V is the direct sum of W and W', and we write vectors as v = w + w' correspondingly, the typical shear is L where L(v) = w + (w' + M(w')) where M is a linear mapping from W' into W. Therefore in matrix terms L can be represented as 2x2 , with blocks on the diagonal I, with M above the diagonal, and 0 below.

Mathematical shears are also called transvections.

In clothing design, fabric may be cut on the shear. This is done by placing the patterns at 45 degrees to the weave of the fabric. Clothing cut on the shear is less stiff and follows the shape of the wearer's body more closely than clothing cut parallel to the weave.