Editing Infinitesimal strain theory (section)

===Principal strains===
It can be shown that it is possible to find a coordinate system (<math>\mathbf{n}_1,\mathbf{n}_2,\mathbf{n}_3</math>) in which the components of the strain tensor are
<math display="block">
   \underline{\underline{\boldsymbol{\varepsilon}}} = \begin{bmatrix} \varepsilon_{1} & 0 & 0 \\
     0 & \varepsilon_{2} & 0 \\
     0 & 0 & \varepsilon_{3} \end{bmatrix} \quad \implies \quad \boldsymbol{\varepsilon} = \varepsilon_{1} \mathbf{n}_1\otimes\mathbf{n}_1 + \varepsilon_{2} \mathbf{n}_2\otimes\mathbf{n}_2 + \varepsilon_{3} \mathbf{n}_3\otimes\mathbf{n}_3 
 </math>
The components of the strain tensor in the (<math>\mathbf{n}_1,\mathbf{n}_2,\mathbf{n}_3</math>) coordinate system are called the '''principal strains''' and the directions <math>\mathbf{n}_i</math> are called the directions of principal strain. Since there are no shear strain components in this coordinate system, the principal strains represent the maximum and minimum stretches of an elemental volume.

If we are given the components of the strain tensor in an arbitrary orthonormal coordinate system, we can find the principal strains using an [[eigenvalue decomposition]] determined by solving the system of equations
<math display="block"> (\underline{\underline{\boldsymbol{\varepsilon}}} - \varepsilon_i~\underline{\underline{\mathbf{I}}})~\mathbf{n}_i = \underline{\mathbf{0}} </math>
This system of equations is equivalent to finding the vector <math>\mathbf{n}_i</math> along which the strain tensor becomes a pure stretch with no shear component.