Principal strains

The principal values (eigenvalues) $\textstyle \varepsilon_1, \varepsilon_2, \varepsilon_3$ of a strain tensor $\textstyle \boldsymbol{\varepsilon}$ are called the principal strains.

If the corresponding principal directions (eigenvectors) are $\textstyle \mathbf{n}_1, \mathbf{n}_2, \mathbf{n}_3$, then

$\boldsymbol{\varepsilon} = \sum^3_{i=1} \varepsilon_i ~ \mathbf{n}_i\otimes\mathbf{n}_i$

is called the spectral decomposition of $\textstyle \boldsymbol{\varepsilon}$.

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