Shear mapping
General shear mappings

For a vector space V and subspace W, a shear fixing W translates all vectors in a direction parallel to W.

To be more precise, if V is the direct sum of W and W ′, and we write vectors as

correspondingly, the typical shear L fixing W is

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