Shear Mapping - Advanced Form

Advanced Form

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 + Mw′) + w ′

where M is a linear mapping from W′ into W. Therefore in block matrix terms L can be represented as

with blocks on the diagonal I (identity matrix), with M above the diagonal, and 0 below.

Read more about this topic:  Shear Mapping

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