Shear mapping
= Shear mapping
{title2=$S_k=\left(\begin{smallmatrix}1&k\\0&1\end{smallmatrix}\right)$}
A horizontal shear fixes the horizontal axis pointwise and sends $(x,y)$ to $(x+ky,y)$. Its <determinant> is one and both <eigenvalues> are one. A nonzero shear preserves area but generally changes lengths and angles. Composing a shear with a <planar rotation> can produce a symmetric stretch; having <determinant> one alone does not make a <linear map> a shear.