Editing Shear mapping (section)

===General shear mappings===
For a [[vector space]] {{mvar|V}} and [[Linear subspace|subspace]] {{mvar|W}}, a shear fixing {{mvar|W}} translates all vectors in a direction parallel to {{mvar|W}}.

To be more precise, if {{mvar|V}} is the [[direct sum of vector spaces|direct sum]] of {{mvar|W}} and {{mvar|W&prime;}}, and we write vectors as

:<math>v=w+w'</math>

correspondingly, the typical shear {{mvar|L}} fixing {{mvar|W}} is
:<math>L(v) = (Lw+Lw') = (w+Mw') + w',</math>
where {{mvar|M}} is a linear mapping from {{mvar|W&prime;}} into {{mvar|W}}. Therefore in [[block matrix]] terms {{mvar|L}} can be represented as

:<math>\begin{pmatrix} I & M \\ 0 & I \end{pmatrix}. </math>