Editing Rotation matrix (section)

=== Voigt notation ===
In [[materials science]], the four-dimensional [[stiffness]] and compliance [[tensors]] are often simplified to a two-dimensional matrix using [[Voigt notation]]. When applying a rotational transform through angle <math> \theta </math> in this notation, the rotation matrix is given by<ref>Clyne, T. W., & Hull, D. (2019). Tensor Analysis of Anisotropic Materials and the Elastic Deformation of Laminae. In An Introduction to Composite Materials (pp. 43–66). chapter, Cambridge: Cambridge University Press.</ref>

:<math> T = \begin{bmatrix}
    \cos^2\theta & \sin^2\theta & 2\sin\theta\cos\theta \\
    \sin^2\theta & \cos^2\theta & 2\sin\theta\cos\theta \\
    -\sin\theta\cos\theta & \sin\theta\cos\theta & \cos^2\theta - \sin^2\theta
  \end{bmatrix}
.</math>

This is particularly useful in [[composite laminate]] design, where plies are often rotated by a certain angle to bring the properties of the laminate closer to [[isotropic]].