Editing Shear mapping (section)

====Composition====
Two or more shear transformations can be combined.

If two shear matrices are <math display="inline">\begin{pmatrix} 1 & \lambda \\ 0 & 1 \end{pmatrix}</math> and <math display="inline">\begin{pmatrix} 1 & 0 \\ \mu & 1 \end{pmatrix}</math>

then their composition matrix is
<math display="block">\begin{pmatrix} 1 & \lambda \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 1 & 0 \\ \mu & 1\end{pmatrix} = \begin{pmatrix} 1 + \lambda\mu & \lambda \\ \mu & 1 \end{pmatrix},</math>
which also has determinant 1, so that area is preserved.

In particular, if <math>\lambda=\mu</math>, we have

<math display="block">\begin{pmatrix} 1 + \lambda^2 & \lambda \\ \lambda & 1 \end{pmatrix},</math>

which is a [[positive definite matrix]].