Shear (mathematics)
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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 fixing W is L where
- L(v) = w + (w′ + M(w′))
where M is a linear mapping from W′ into W. Therefore in block matrix terms L can be represented as 2×2 , with blocks on the diagonal I (identity matrix), with M above the diagonal, and 0 below.
Mathematical shears are also called transvections.